A335937 Infinitary pseudoperfect numbers (A306983) that equal to the sum of a subset of their aliquot infinitary divisors in a single way.

6, 60, 72, 78, 88, 90, 96, 102, 104, 114, 138, 150, 174, 186, 222, 246, 258, 282, 294, 318, 354, 366, 402, 426, 438, 474, 486, 498, 534, 582, 606, 618, 642, 654, 678, 726, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 1014, 1038, 1074, 1086, 1146, 1158, 1182, 1194

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..3000

Example

72 is a term since its set of infinitary aliquot divisors is {1, 2, 4, 8, 9, 18, 36}, and {1, 8, 9, 18, 36} is its only subset whose sum is equal to 72.

Mathematica

idivs[x_] := If[x == 1, 1, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infpspQ[n_] := Module[{d = Most @ idivs[n], x}, Plus @@ d >= n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 1]; Select[Range[2, 1200], infpspQ]

Crossrefs

The infinitary version of A064771.

Subsequence of A306983.

A007357 is a subsequence.

Similar sequences: A295829, A295830, A321145.

Cf. A049417, A077609, A335199.

Sequence in context: A335202 A061475 A295830 * A136937 A295829 A074452

Adjacent sequences: A335934 A335935 A335936 * A335938 A335939 A335940

Keyword

nonn

Author

Amiram Eldar, Jun 30 2020

Status

approved