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

Author

Amiram Eldar, May 26 2020

Keywords

• nonn

Examples

			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}.
		

Crossrefs

The infinitary version of A083209.

Subsequence of A335197.

Programs

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 *)