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%I A074122 #4 Dec 05 2013 19:55:33
%S A074122 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,
%T A074122 31,20,17,42,7,68,21,26,3,16,30,53,6,73,18,84,19,26,77,32,5,83,3,55,
%U A074122 16,107,1,44,5,40,7,207,17,41,17,14,23,49,100,46,34,36,47,216,50,17,7,58
%N A074122 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.
%C A074122 a(n) = 1 for n: 1,2,4,6,8,55,154,616,(10^4).
%e A074122 (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), ...
%t A074122 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
%Y A074122 Cf. A002808, A074130, A074120, A074121, A074123.
%K A074122 nonn
%O A074122 1,3
%A A074122 _Amarnath Murthy_, Aug 27 2002
%E A074122 Edited, corrected and extended by _Robert G. Wilson v_, Aug 29 2002

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