A335199 Infinitary Zumkeller numbers (A335197) whose set of infinitary divisors can be partitioned into two disjoint sets of equal sum in a single way.

6, 56, 60, 70, 72, 88, 90, 104, 3040, 3230, 3770, 4030, 4510, 5170, 5390, 5800, 5830, 6808, 7144, 7192, 7400, 7912, 8056, 8968, 9272, 9656, 9928, 10744, 10792, 11016, 11096, 11288, 11392, 12104, 12416, 12928, 13184, 13192, 13696, 13736, 13952, 14008, 14464, 14552

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Example

6 is a term since there is only one partition of its set of nonunitary divisors, {1, 2, 3, 6}, into two disjoint sets of equal sum: {1, 2, 3} and {6}.

Mathematica

infdivs[n_] := If[n == 1, {1}, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infZumQ[n_] := Module[{d = infdivs[n], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] == 2]]; Select[Range[15000], infZumQ] (* after Michael De Vlieger at A077609 *)

Crossrefs

The infinitary version of A083209.

Subsequence of A335197.

Sequence in context: A183594 A140790 A335217 * A137033 A045526 A164579

Adjacent sequences: A335196 A335197 A335198 * A335200 A335201 A335202

Keyword

nonn

Author

Amiram Eldar, May 26 2020

Status

approved