A074123 Group successively larger composite numbers so that the sum of the n-th group is a multiple of n. Sequence gives group sum divided by n for the n-th group.

4, 3, 9, 3, 9, 3, 9, 3, 30, 33, 18, 65, 178, 46, 120, 225, 224, 175, 341, 175, 340, 121, 106, 39, 207, 251, 53, 307, 434, 291, 252, 649, 111, 1132, 372, 468, 54, 285, 541, 996, 115, 1446, 371, 1803, 424, 583, 1790, 770, 120, 2037, 75, 1388, 408, 2816, 27, 1188

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = A074120(n)/n.

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];

Crossrefs

Cf. A002808, A074131, A074120, A074121, A074122.

Sequence in context: A236099 A155536 A232814 * A016704 A131896 A114380

Adjacent sequences: A074120 A074121 A074122 * A074124 A074125 A074126

Keyword

nonn

Author

Amarnath Murthy, Aug 27 2002

Extensions

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

a(46) onward corrected by Sean A. Irvine, Jan 12 2025

Status

approved