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A335936
Infinitary weird numbers (A306984) whose number of divisors is not a power of 2.
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
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.
Sequence in context: A057850 A058325 A224688 * A335939 A328562 A340109
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 30 2020
EXTENSIONS
More terms from Amiram Eldar, Mar 25 2023
STATUS
approved