A335936 Infinitary weird numbers (A306984) whose number of divisors is not a power of 2.

5390, 7400, 11830, 17920, 20230, 25270, 37030, 43750, 58870, 67270, 95830, 117670, 129430, 154630, 168070, 196630, 243670, 260470, 314230, 352870, 373030, 436870, 459270, 482230, 554470, 658630, 714070, 742630, 801430, 831670, 893830, 1024870, 1129030, 1201270

Offset

1,1

Comments

Weird numbers (A006037) whose number of divisors is a power of 2 (A036537) are also infinitary weird numbers (A306983), since all of their divisors are infinitary.

Links

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

Mathematica

fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, 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]; infabQ[n_] := isigma[n] > 2*n; idivs[x_] := If[x == 1, 1, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infwQ[n_] := infabQ[n] && Module[{d = Most @ idivs[n]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; pow2Q[n_] := n == 2^IntegerExponent[n, 2]; seq = {}; Do[If[!pow2Q[DivisorSigma[0, n]] && infwQ[n], AppendTo[sm n]], {n, 1, 10^5}]; s

Crossrefs

Intersection of A162643 and A306984.

Cf. A006037, A036537, A077609, A335935.

Sequence in context: A057850 A058325 A224688 * A335939 A328562 A340109

Adjacent sequences: A335933 A335934 A335935 * A335937 A335938 A335939

Keyword

nonn

Author

Amiram Eldar, Jun 30 2020

Extensions

More terms from Amiram Eldar, Mar 25 2023

Status

approved