A348527 Noninfinitary Zumkeller numbers: numbers whose set of noninfinitary divisors is nonempty and can be partitioned into two disjoint sets of equal sum.

48, 80, 96, 112, 150, 180, 240, 252, 294, 336, 360, 396, 432, 468, 480, 486, 504, 528, 560, 600, 612, 624, 630, 672, 684, 720, 726, 768, 792, 810, 816, 828, 864, 880, 912, 936, 960, 1008, 1014, 1040, 1044, 1050, 1056, 1104, 1116, 1120, 1134, 1176, 1200, 1232, 1248

Offset

1,1

Comments

The smallest odd term is a(104) = 2475.

Links

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

Example

48 is a term since its set of noninfinitary divisors, {2, 4, 6, 8, 12, 24}, can be partitioned into the two disjoint sets, {2, 6, 8, 12} and {4, 24}, whose sums are equal: 2 + 6 + 8 + 12 = 4 + 24 = 28.

Mathematica

nidiv[1] = {}; nidiv[n_] := Complement[Divisors[n], Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; nizQ[n_] := Module[{d = nidiv[n], sum, x}, sum = Plus @@ d; sum > 0 && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]; Select[Range[1250], !IntegerQ@ Log2@ DivisorSigma[0, #] && nizQ[#] &]

Crossrefs

Cf. A348271, A348274, A348341.

Similar sequences: A083207, A290466, A335215, A335142, A335197, A335218.

Sequence in context: A261553 A335281 A335196 * A362969 A110229 A108608

Adjacent sequences: A348524 A348525 A348526 * A348528 A348529 A348530

Keyword

nonn

Author

Amiram Eldar, Oct 21 2021

Status

approved