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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. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The infinitary version of A171641.

LINKS

Table of n, a(n) for n=1..30.

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

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)