

A335937


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


1



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
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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



