A334975 Odd infinitary admirable numbers: the odd terms of A334974.

945, 43065, 46035, 80535, 354585, 403095, 430815, 437745, 442365, 2305875, 3525795, 4404105, 4891887, 5388495, 5927985, 6126645, 6220665, 6375105, 6537375, 7853625, 8109585, 8731125, 9071865, 9338595, 9784125, 13241745, 23760555, 33381855, 34592805, 35642295

Offset: 1

Author

Amiram Eldar, May 18 2020

Keywords

• nonn

Comments

Of the first 10^4 infinitary admirable numbers only 9 are odd.

Crossrefs

The infinitary version of A109729.

Intersection of A005408 and A334974.

Subsequence of A127666.

Cf. A329188, A334973.

Programs

Mathematica

fun[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 @@ fun @@@ FactorInteger[n]; infDivQ[n_, 1] = True; infDivQ[n_, d_] := BitAnd[IntegerExponent[n, First /@ (f = FactorInteger[d])], (e = Last /@ f)] == e; infAdmQ[n_] := (ab = isigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && infDivQ[n, ab/2]; Select[Range[1, 5*10^5, 2], infAdmQ]