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A335936 Infinitary weird numbers (A306984) whose number of divisors is not a power of 2. 1
5390, 7400, 11830, 17920, 20230, 25270, 37030, 43750, 58870, 67270, 95830, 117670, 129430, 154630, 168070, 196630, 243670, 260470, 314230 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..19.

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

Subsequence of 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,more

AUTHOR

Amiram Eldar, Jun 30 2020

STATUS

approved

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Last modified July 4 22:49 EDT 2022. Contains 355086 sequences. (Running on oeis4.)