

A335197


Infinitary Zumkeller numbers: numbers whose set of infinitary divisors can be partitioned into two disjoint sets of equal sum.


6



6, 24, 30, 40, 42, 54, 56, 60, 66, 70, 72, 78, 88, 90, 96, 102, 104, 114, 120, 138, 150, 168, 174, 186, 210, 216, 222, 246, 258, 264, 270, 280, 282, 294, 312, 318, 330, 354, 360, 366, 378, 384, 390, 402, 408, 420, 426, 438, 440, 456, 462, 474, 480, 486, 498, 504
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OFFSET

1,1


LINKS

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


EXAMPLE

6 is a term since its set of infinitary divisors, {1, 2, 3, 6}, can be partitioned into the two disjoint sets, {1, 2, 3} and {6}, whose sum is equal: 1 + 2 + 3 = 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]] > 0]]; Select[Range[500], infZumQ] (* after Michael De Vlieger at A077609 *)


CROSSREFS

The infinitary version of A083207.
Subsequence of A129656.
Cf. A077609, A323344.
Sequence in context: A114274 A335215 A292985 * A306983 A234648 A110926
Adjacent sequences: A335194 A335195 A335196 * A335198 A335199 A335200


KEYWORD

nonn


AUTHOR

Amiram Eldar, May 26 2020


STATUS

approved



