A348523 Numbers that are both infinitary and noninfinitary abundant numbers.

960, 1440, 1800, 2016, 2400, 2940, 3240, 3528, 3780, 4536, 4860, 6720, 7260, 8640, 10080, 10140, 10560, 12096, 12480, 12600, 13860, 14784, 15120, 15360, 15840, 16320, 16380, 16800, 17472, 17640, 18240, 18480, 18720, 18900, 19008, 19800, 20160, 21420, 21600, 21840

Offset: 1

Author

Amiram Eldar, Oct 21 2021

Keywords

• nonn

Comments

Apparently, the smallest odd term is 9170790153525.

Examples

			960 is a term since A049417(960) = 2040 > 2*960 = 1920 and A348271(960) = 1008 > 960.
		

Links

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

Crossrefs

Intersection of A129656 and A348274.

Subsequence of A068403.

Cf. A049417, A348271.

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]; q[n_] := (i = isigma[n]) > 2*n && DivisorSigma[1, n] - i > n; Select[Range[10^4], q]