A348274 Noninfinitary abundant numbers: numbers k such that A348271(k) > k.

36, 48, 80, 144, 180, 240, 252, 288, 300, 324, 336, 396, 400, 432, 468, 528, 560, 576, 588, 612, 624, 684, 720, 768, 784, 816, 828, 880, 900, 912, 960, 1008, 1040, 1044, 1104, 1116, 1200, 1232, 1260, 1280, 1296, 1332, 1360, 1392, 1440, 1456, 1476, 1488, 1520, 1548

Offset: 1

Author

Amiram Eldar, Oct 09 2021

Keywords

• nonn

Comments

The first odd term is a(3577) = 99225.

The number of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 3, 31, 360, 3605, 36160, 360840, 3618980, 36144059, ... Apparently this sequence has an asymptotic density 0.0361...

Examples

			36 is a term since A348271(36) = 41 > 36.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A348271, A327633.

Subsequence of A005101.

Similar sequences: A034683, A064597, A129575, A129656, A292982.

Programs

Mathematica

f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := DivisorSigma[1,n] - isigma[n]; Select[Range[1500], s[#] > # &]