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A127192
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Triangle read by rows: square of A054523.
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2
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1, 2, 1, 4, 0, 1, 5, 2, 0, 1, 8, 0, 0, 0, 1, 8, 4, 2, 0, 0, 1, 12, 0, 0, 0, 0, 0, 1, 12, 5, 0, 2, 0, 0, 0, 1, 16, 0, 4, 0, 0, 0, 0, 0, 1, 16, 8, 0, 0, 2, 0, 0, 0, 0, 1, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20, 8, 5, 4, 0, 2, 0, 0, 0, 0, 0, 1, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Row sums = A018804: (1, 3, 5, 8, 9, 15, ...), sum of gcd(k,n) for 1<= k <= n. Left column = A029935: (1, 2, 4, 5, 8, 8, 12, 12, ...). A127192 * d(n) = d(n) * n, or A127192 * A000005 = A038040 = (1, 4, 6, 12, 10, 24, 14, ...).
Column k contains terms of A029935 interspersed with (k-1) zeros.
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LINKS
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EXAMPLE
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First few rows of the triangle:
1;
2, 1;
4, 0, 1;
5, 2, 0, 1;
8, 0, 0, 0, 1;
8, 4, 2, 0, 0, 1;
12, 0, 0, 0, 0, 0, 1;
12, 5, 0, 2, 0, 0, 0, 1;
16, 0, 4, 0, 0, 0, 0, 0, 1;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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a(20) ff. corrected and more terms from Georg Fischer, May 31 2023
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STATUS
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approved
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