

A334405


Pseudoperfect numbers k such that there is a subset of divisors of k whose sum is 2*k and for each d in this subset k/d is also in it.


3



6, 28, 36, 60, 84, 90, 120, 156, 210, 216, 240, 252, 270, 300, 312, 330, 336, 352, 396, 420, 468, 480, 496, 504, 540, 546, 552, 576, 588, 594, 600, 616, 624, 630, 648, 660, 672, 714, 720, 756, 760, 780, 784, 792, 816, 840, 864, 888, 900, 924, 960, 972, 1000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Includes all the perfect numbers (A000396).


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1650


FORMULA

36 is a term since {1, 2, 3, 12, 18, 36} is a subset of its divisors whose sum is 72 = 2 * 36, and for each divisor d in this subset 36/d is also in it: 1 * 36 = 2 * 18 = 3 * 12 = 36.


MATHEMATICA

seqQ[n_] := Module[{d = Divisors[n]}, nd = Length[d]; divpairs = If[EvenQ[nd], d[[1 ;; nd/2]] + d[[1 ;; nd/2 + 1 ;; 1]], Join[d[[1 ;; (nd  1)/2]] + d[[1 ;; (nd + 3)/2 ;; 1]], {d[[(nd + 1)/2]]}]]; SeriesCoefficient[Series[Product[1 + x^divpairs[[i]], {i, Length[divpairs]}], {x, 0, 2*n}], 2*n] > 0]; Select[Range[1000], seqQ]


CROSSREFS

Subsequence of A005835.
A000396 is a subsequence.
Sequence in context: A272971 A117948 A252234 * A242344 A344588 A247111
Adjacent sequences: A334402 A334403 A334404 * A334406 A334407 A334408


KEYWORD

nonn


AUTHOR

Amiram Eldar, Apr 27 2020


STATUS

approved



