A152616 Numbers k such that exactly three subsets of proper divisors of k sum to k.

30, 40, 54, 350, 380, 414, 500, 532, 544, 558, 608, 620, 644, 666, 726, 740, 1372, 2002, 2190, 2368, 2370, 2490, 2624, 2670, 2910, 3030, 3090, 3162, 3210, 3250, 3270, 3390, 3410, 3430, 3810, 3880, 3930, 4040, 4110, 4120, 4170, 4280, 4360, 4470, 4520, 4530

Offset

1,1

Comments

Or numbers k such that A065205(k) = 3.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

The proper divisors of 30 = {1,2,3,5,6,10,15} and 30 = 5+10+15 = 2+3+10+15 = 1+3+5+6+15.

Mathematica

seqQ[n_] := Module[{d = Most[Divisors[n]]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 3]; Select[Range[1000], seqQ[#] &] (* Amiram Eldar, Jan 13 2020 *)

Crossrefs

Cf. A064771, A065205, A065235, A152615.

Sequence in context: A223727 A025376 A280640 * A309306 A103250 A181638

Adjacent sequences: A152613 A152614 A152615 * A152617 A152618 A152619

Keyword

nonn

Author

Zak Seidov, Oct 29 2009

Status

approved