A348527 - OEIS

%I #10 Oct 22 2021 16:14:56

%S 48,80,96,112,150,180,240,252,294,336,360,396,432,468,480,486,504,528,

%T 560,600,612,624,630,672,684,720,726,768,792,810,816,828,864,880,912,

%U 936,960,1008,1014,1040,1044,1050,1056,1104,1116,1120,1134,1176,1200,1232,1248

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

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

%H Amiram Eldar, <a href="/A348527/b348527.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%t 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[#] &]

%Y Cf. A348271, A348274, A348341.

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

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 21 2021