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.

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

Offset

1,3

Comments

a(n) = 1 for n: 1,2,4,6,8,55,154,616,(10^4).

Links

Table of n, a(n) for n=1..76.

Example

(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), ...

Mathematica

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

Crossrefs

Cf. A002808, A074130, A074120, A074121, A074123.

Sequence in context: A070039 A227991 A319137 * A372834 A335182 A319992

Adjacent sequences: A074119 A074120 A074121 * A074123 A074124 A074125

Keyword

nonn

Author

Amarnath Murthy, Aug 27 2002

Extensions

Edited, corrected and extended by Robert G. Wilson v, Aug 29 2002

Status

approved