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 A348527 Noninfinitary Zumkeller numbers: numbers whose set of noninfinitary divisors is nonempty and can be partitioned into two disjoint sets of equal sum. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 21 04:54 EDT 2024. Contains 371850 sequences. (Running on oeis4.)