

A308605


Distinct subset sums of the subsets of the set of divisors of n.


0



2, 4, 4, 8, 4, 13, 4, 16, 8, 16, 4, 29, 4, 16, 16, 32, 4, 40, 4, 43, 16, 16, 4, 61, 8, 16, 16, 57, 4, 73, 4, 64, 16, 16, 16, 92, 4, 16, 16, 91, 4, 97, 4, 64, 56, 16, 4, 125, 8, 64, 16, 64, 4, 121, 16, 121, 16, 16, 4, 169, 4, 16, 60, 128, 16, 145, 4, 64, 16, 143, 4, 196, 4, 16, 64, 64
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OFFSET

1,1


COMMENTS

Conjecture: When the terms are sorted and the duplicates deleted a supersequence of A030058 is obtained. Note that A030058 is a result of the same operation applied to A030057.


LINKS

Table of n, a(n) for n=1..76.


FORMULA

a(n) = 1 + A119347(n).  Rémy Sigrist, Jun 10 2019


EXAMPLE

The subsets of the set of divisors of 6 are {{},{1},{2},{3},{6},{1,2},{1,3},{1,6},{2,3},{2,6},{3,6},{1,2,3},{1,2,6},{1,3,6},{2,3,6},{1,2,3,6}}, with the following sums {0,1,2,3,6,3,4,7,5,8,9,6,9,10,11,12}, of which 13 are distinct. Therefore, a(6)=13.


MATHEMATICA

f[n_]:=Length[Union[Total/@Subsets[Divisors[n]]]]; f/@Range[100]


CROSSREFS

Cf. A030057, A030058, A119347.
Sequence in context: A131136 A117973 A140434 * A107748 A005884 A229913
Adjacent sequences: A308602 A308603 A308604 * A308606 A308607 A308608


KEYWORD

nonn


AUTHOR

Ivan N. Ianakiev, Jun 10 2019


STATUS

approved



