A327947 Nonunitary pseudoperfect numbers (A327945) that equal to the sum of a subset of their nonunitary divisors in more ways than any smaller nonunitary pseudoperfect number.

24, 48, 72, 96, 144, 216, 240, 288, 360, 480, 720, 1080, 1440, 2160, 2880, 3600, 4320, 5040, 7200, 7560, 10080, 15120, 20160, 25200, 30240

Offset

1,1

Comments

The nonunitary version of A065218.

The corresponding numbers of ways are 1, 2, 4, 5, 15, 28, 34, 63, 211, 279, 6025, 17436, 187794, 2035726, 5965563, 36449982, 250420995, 3426156924, 8991176276, 37016127059, 6770551810345, 1095548357870254, 13524344273940115, 604532928571438678, 33370817837127087825, ...

Links

Table of n, a(n) for n=1..25.

Example

24 is the least number which is the sum of its nonunitary divisor, thus a(1) = 24.
48 is the least number which is the sum of a subset of its nonunitary divisor in two ways: 24 + 12 + 8 + 4 and 24 + 12 + 8 + 4 + 2, thus a(2) = 48.

Mathematica

nudiv[n_] := Module[{d = Divisors[n]}, Select[d, GCD[#, n/#] > 1 &]]; s = {}; cm = 0; 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 > cm, cm = c; AppendTo[s, n]], {n, 1, 1000}]; s

Crossrefs

Cf. A064591, A064597, A065218, A327945, A327946.

Sequence in context: A008606 A317971 A141767 * A288639 A280097 A054734

Adjacent sequences: A327944 A327945 A327946 * A327948 A327949 A327950

Keyword

nonn,more

Author

Amiram Eldar, Sep 30 2019

Status

approved