A323344 Numbers k whose infinitary divisors have an even sum which is larger than 2k, but they cannot be partitioned into two disjoint parts whose sums are equal.

2394, 7544, 10184, 1452330, 2154584, 5021912, 5747994, 5771934, 5786298, 5800662, 5834178, 5843754, 5858118, 5886846, 5905998, 5920362, 5929938, 5992182, 6035274, 6059214, 6078366, 6087942, 6102306, 6107094, 6121458, 6174126, 6202854, 6207642, 6245946, 6265098

Offset

1,1

Comments

The infinitary version of A171641.

Links

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

Mathematica

infdivs[x_] := If[x == 1, 1, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]] ; 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[n_] := If[n == 1, 1, Times @@ (fun @@@ FactorInteger[n])]; seq={}; Do[s=isigma[n]; If[OddQ[s] || s<=2n, Continue[]]; div = infdivs[n]; If[Coefficient[Times @@ (1 + x^div) // Expand, x, s/2] == 0, AppendTo[seq, n]], {n, 1, 100000}]; seq (* after Michael De Vlieger at A077609 *)

Crossrefs

Cf. A049417, A077609, A129656, A171641, A323341, A323342, A323343.

Sequence in context: A098680 A226149 A115931 * A323341 A108055 A286342

Adjacent sequences: A323341 A323342 A323343 * A323345 A323346 A323347

Keyword

nonn

Author

Amiram Eldar, Jan 11 2019

Status

approved