A327945 Nonunitary pseudoperfect numbers: numbers that are equal to the sum of a subset of their nonunitary divisors.

24, 36, 48, 72, 80, 96, 108, 112, 120, 144, 160, 168, 180, 192, 200, 216, 224, 240, 252, 264, 288, 300, 312, 320, 324, 336, 352, 360, 384, 392, 396, 400, 408, 416, 432, 448, 456, 468, 480, 504, 528, 540, 552, 560, 576, 588, 600, 612, 624, 640, 648, 672, 684

Offset

1,1

Comments

The nonunitary version of A005835.

Links

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

Example

36 is in the sequence since its nonunitary divisors are 2, 3, 6, 12, 18 and 36 = 6 + 12 + 18.

Mathematica

nudiv[n_] := Module[{d = Divisors[n]}, Select[d, GCD[#, n/#] > 1 &]]; s = {}; Do[d = nudiv[n]; If[Total[d] < n, Continue[]]; c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c > 0, AppendTo[s, n]], {n, 1, 700}]; s

Crossrefs

Supersequence of A064591.

Cf. A005835, A064597, A293188, A292985, A306983.

Sequence in context: A067766 A306776 A300794 * A078347 A187516 A165602

Adjacent sequences: A327942 A327943 A327944 * A327946 A327947 A327948

Keyword

nonn

Author

Amiram Eldar, Sep 30 2019

Status

approved