Search: a074121 -id:a074121
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A074120
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Group successively larger composite numbers so that the sum of the n-th group is a multiple of n. Sequence gives the sum of the terms in the n-th group.
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+10
3
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4, 6, 27, 12, 45, 18, 63, 24, 270, 330, 198, 780, 2314, 644, 1800, 3600, 3808, 3150, 6479, 3500, 7140, 2662, 2438, 936, 5175, 6526, 1431, 8596, 12586, 8730, 7812, 20768, 3663, 38488, 13020, 16848, 1998, 10830, 21099, 39840, 4715, 60732, 15953
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OFFSET
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1,1
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LINKS
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EXAMPLE
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(4), (6), (8, 9, 10), (12), (14, 15, 16), (18), (20, 21, 22), (24), (25, 26, 27, 28, 30, 32, 33, 34, 35), (36, 38, 39, 40, 42, 44, 45, 46), (48, 49, 50, 51), ...
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MATHEMATICA
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NextComposite[n_] := Block[{k = n + 1}, While[PrimeQ[k], k++ ]; k]; a = {}; k = 1; Do[s = 0; While[k = NextComposite[k]; s = s + k; !IntegerQ[s/n], ]; a = Append[a, s], {n, 1, 45}]; a
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A074122
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Group successively larger composite numbers so that the sum of the n-th group is a multiple of n. Sequence gives the number of terms in the n-th group.
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+10
3
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1, 1, 3, 1, 3, 1, 3, 1, 9, 8, 4, 13, 27, 6, 15, 25, 22, 16, 29, 14, 26, 9, 8, 3, 16, 19, 4, 23, 31, 20, 17, 42, 7, 68, 21, 26, 3, 16, 30, 53, 6, 73, 18, 84, 19, 26, 77, 32, 5, 83, 3, 55, 16, 107, 1, 44, 5, 40, 7, 207, 17, 41, 17, 14, 23, 49, 100, 46, 34, 36, 47, 216, 50, 17, 7, 58
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graph;
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listen;
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OFFSET
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1,3
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COMMENTS
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a(n) = 1 for n: 1,2,4,6,8,55,154,616,(10^4).
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LINKS
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EXAMPLE
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(4), (6), (8, 9, 10), (12), (14, 15, 16), (18), (20, 21, 22), (24), (25, 26, 27, 28, 30, 32, 33, 34, 35), (36, 38, 39, 40, 42, 44, 45, 46), (48, 49, 50, 51), ...
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MATHEMATICA
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NextComposite[n_] := Block[{k = n + 1}, While[PrimeQ[k], k++ ]; k]; a = {}; k = 1; Do[s = 0; c = 0; While[k = NextComposite[k]; s = s + k; !IntegerQ[s/n], c++ ]; a = Append[a, c + 1], {n, 1, 80}]; a
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A074123
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Group successively larger composite numbers so that the sum of the n-th group is a multiple of n. Sequence gives group sum divided by n for the n-th group.
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+10
3
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4, 3, 9, 3, 9, 3, 9, 3, 30, 33, 18, 65, 178, 46, 120, 225, 224, 175, 341, 175, 340, 121, 106, 39, 207, 251, 53, 307, 434, 291, 252, 649, 111, 1132, 372, 468, 54, 285, 541, 996, 115, 1446, 371, 1803, 424, 200, 526, 185, 488, 243, 149, 190, 55, 224, 486, 188, 170
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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(4), (6), (8, 9, 10), (12), (14, 15, 16), (18), (20, 21, 22), (24), (25, 26, 27, 28, 30, 32, 33, 34, 35), (36, 38, 39, 40, 42, 44, 45, 46), (48, 49, 50, 51), ...
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MATHEMATICA
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NextComposite[n_] := Block[{k = n + 1}, While[PrimeQ[k], k++ ]; k];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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