A327946 - OEIS

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A327946

Nonunitary pseudoperfect numbers (A327945) that equal to the sum of a subset of their nonunitary divisors in a single way.

24, 36, 80, 112, 200, 312, 352, 392, 408, 416, 456, 552, 588, 684, 696, 744, 888, 984, 1032, 1088, 1116, 1128, 1216, 1272, 1332, 1416, 1464, 1472, 1548, 1608, 1692, 1704, 1752, 1856, 1896, 1908, 1936, 1984, 1992, 2124, 2136, 2196, 2288, 2328, 2412, 2424, 2472

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OFFSET

1,1

COMMENTS

The nonunitary version of A064771.

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

The nonunitary divisors of 36 are {2, 3, 6, 12, 18), and {6, 12, 18} is the only subset that sums to 36.

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 == 1, AppendTo[s, n]], {n, 1, 700}]; s

CROSSREFS

Cf. A064771, A064591, A064597, A295829, A327945.

Sequence in context: A193069 A347422 A278474 * A288949 A108190 A185489

Adjacent sequences: A327943 A327944 A327945 * A327947 A327948 A327949

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 30 2019

STATUS

approved