A335935 Infinitary pseudoperfect numbers (A306983) whose number of divisors is not a power of 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

Offset: 1

Author

Amiram Eldar, Jun 30 2020

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A005835 and A306983.

Cf. A036537, A077609, A335198.

Programs

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[#] &]