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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.
3

%I #4 Dec 05 2013 19:55:33

%S 4,6,27,12,45,18,63,24,270,330,198,780,2314,644,1800,3600,3808,3150,

%T 6479,3500,7140,2662,2438,936,5175,6526,1431,8596,12586,8730,7812,

%U 20768,3663,38488,13020,16848,1998,10830,21099,39840,4715,60732,15953

%N 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.

%e (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 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

%Y Cf. A002808, A074128, A074121, A074122 A074123.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 27 2002

%E Edited, corrected and extended by _Robert G. Wilson v_, Aug 29 2002