

A074122


Group successively larger composite numbers so that the sum of the nth group is a multiple of n. Sequence gives the number of terms in the nth group.


3



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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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 * A335182 A319992 A255894
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



