A375154 Least k with exactly n partitions k = x + y + z satisfying sigma(k) = sigma(x) + sigma(y) + sigma(z).

5, 25, 33, 39, 38, 58, 65, 86, 123, 85, 82, 92, 98, 152, 99, 158, 106, 135, 153, 145, 215, 186, 142, 189, 235, 178, 185, 165, 147, 315, 274, 231, 214, 305, 171, 332, 207, 290, 310, 344, 266, 358, 583, 297, 261, 278, 285, 488, 255, 334, 302, 369, 309, 2888, 284

Offset

1,1

Comments

No other prime apart from initial 5.

Links

David A. Corneth, Table of n, a(n) for n = 1..764

Example

a(7) = 65 and 65 has 7 partitions of three numbers, x, y and z, for which sigma(65) = sigma(x) + sigma(y) + sigma(z) = 84. In fact:
sigma(2) + sigma(14) + sigma(49) = 3 + 24 + 57 = 84;
sigma(3) + sigma(7) + sigma(55) = 4 + 8 + 72 = 84;
sigma(3) + sigma(23) + sigma(39) = 4 + 24 + 56 = 84;
sigma(5) + sigma(5) + sigma(55) = 6 + 6 + 72 = 84;
sigma(7) + sigma(19) + sigma(39) = 8 + 20 + 56 = 84;
sigma(10) + sigma(14) + sigma(41) = 18 + 24 + 42 = 84;
sigma(13) + sigma(13) + sigma(39) = 14 + 14 + 56 = 84;
Furthermore 65 is the minimum number to have this property.

Mathematica

f[n_] := Count[IntegerPartitions[n, {3}], _?(Total[DivisorSigma[1, #]] == DivisorSigma[1, n] &)]; With[{s = Array[f, 600]}, TakeWhile[FirstPosition[s, #] & /@ Range[Max[s]] // Flatten, !MissingQ[#] &]] (* Amiram Eldar, Aug 02 2024 *)

Crossrefs

Cf. A000203, A211223, A211224, A211225, A373047.

Sequence in context: A029475 A332657 A070391 * A084967 A249827 A343734

Adjacent sequences: A375151 A375152 A375153 * A375155 A375156 A375157

Keyword

nonn

Author

Paolo P. Lava, Aug 01 2024

Status

approved