

A335935


Infinitary pseudoperfect numbers (A306983) whose number of divisors is not a power of 2.


2



60, 72, 90, 96, 150, 294, 360, 420, 480, 486, 504, 540, 600, 630, 660, 672, 726, 756, 780, 792, 864, 924, 936, 960, 990, 1014, 1020, 1050, 1056, 1092, 1120, 1140, 1152, 1170, 1176, 1188, 1224, 1248, 1344, 1350, 1368, 1380, 1386, 1400, 1428, 1440, 1470, 1500, 1530
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OFFSET

1,1


COMMENTS

Pseudoperfect numbers (A005835) whose number of divisors is a power of 2 (A036537) are also infinitary pseudoperfect numbers (A306983), since all of their divisors are infinitary.
First differs from A335198 at n = 77.


LINKS

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


EXAMPLE

60 is a term since its number of divisors is 12 which is not a power of 2, so not all of its divisors are infinitary, and it is the sum of its infinitary divisors: 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.


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] > 0]; pow2Q[n_] := n == 2^IntegerExponent[n, 2]; Select[Range[2, 500], !pow2Q[DivisorSigma[0, #]] && infpspQ[#] &]


CROSSREFS

Subsequence of A005835 and A306983.
Cf. A036537, A077609, A335198.
Sequence in context: A068350 A265712 A335198 * A347935 A347938 A114837
Adjacent sequences: A335932 A335933 A335934 * A335936 A335937 A335938


KEYWORD

nonn


AUTHOR

Amiram Eldar, Jun 30 2020


STATUS

approved



