A334973 Odd bi-unitary admirable numbers: the odd terms of A334972.

945, 43065, 46035, 48195, 80535, 354585, 403095, 430815, 437745, 442365, 458055, 2305875, 3525795, 4404105, 4891887, 5388495, 5803245, 6126645, 6220665, 6375105, 6537375, 7853625, 7981875, 8109585, 8731125, 9071865, 9338595, 9784125, 13241745, 13351635, 23760555

Offset: 1

Author

Amiram Eldar, May 18 2020

Keywords

• nonn

Comments

Of the first 10^4 bi-unitary admirable numbers only 11 are odd.

Crossrefs

The bi-unitary version of A109729.

Intersection of A005408 and A334972.

Subsequence of A293186.

Cf. A329188, A334975.

Programs

Mathematica

fun[p_, e_] := If[OddQ[e], (p^(e + 1) - 1)/(p - 1), (p^(e + 1) - 1)/(p - 1) - p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); buDivQ[n_, 1] = True; buDivQ[n_, div_] := If[Mod[#2, #1] == 0, Last@Apply[Intersection, Map[Select[Divisors[#], Function[d, CoprimeQ[d, #/d]]] &, {#1, #2/#1}]] == 1, False] & @@ {div, n}; buAdmQ[n_] := (ab = bsigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && buDivQ[n, ab/2]; Select[Range[1, 5*10^5, 2], buAdmQ]