A199919 Number of distinct sums of distinct divisors of n when positive and negative divisors are allowed.

3, 7, 9, 15, 9, 25, 9, 31, 27, 37, 9, 57, 9, 49, 49, 63, 9, 79, 9, 85, 65, 49, 9, 121, 27, 49, 81, 113, 9, 145, 9, 127, 81, 49, 69, 183, 9, 49, 81, 181, 9, 193, 9, 169, 157, 49, 9, 249, 27, 187, 81, 197, 9, 241, 69, 241, 81, 49, 9, 337, 9, 49, 209, 255, 81, 289

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Bernard Jacobson, Sums of distinct divisors and sums of distinct units, Proc. Amer. Math. Soc. 15 (1964), 179-183

David A. Corneth, PARI program

Formula

a(A005153(n)) = 2*sigma(A005153(n)) + 1. - David A. Corneth, May 19 2021

a(p) = 9 for odd primes p. - Antti Karttunen, May 19 2021

Example

a(2)=7 because the signed divisors of 2 are -2, -1, 1 and 2 and their all possible sums are -1, -2, -3, 0, 1, 2, 3.
a(3)=9 because the signed divisors of 3 are -3, -1, 1 and 3 and their all possible sums are -1, -2, -3, -4, 0, 1, 2, 3, 4.

Mathematica

dsdd[n_]:=Module[{divs=Divisors[n]}, Length[Union[Total/@Subsets[ Join[ divs, -divs], 2Length[divs]]]]]; Array[dsdd, 70] (* Harvey P. Dale, Jan 19 2015 *)

Prog

(PARI)
A199919(n) = { my(ds=concat(apply(x -> -x, divisors(n)), divisors(n)), m=Map(), s, u=0); for(i=0, (2^#ds)-1, s = sumbybits(ds, i); if(!mapisdefined(m, s), mapput(m, s, s); u++)); (u); }; \\ Slow!
sumbybits(v, b) = { my(s=0, i=1); while(b>0, s += (b%2)*v[i]; i++; b >>= 1); (s); }; \\ Antti Karttunen, May 19 2021
(PARI) See PARI-link \\ David A. Corneth, May 20 2021

Crossrefs

Cf. A005153, A119347.

Sequence in context: A172987 A118556 A279617 * A346303 A178207 A210532

Adjacent sequences: A199916 A199917 A199918 * A199920 A199921 A199922

Keyword

nonn,look

Author

Michel Marcus, Dec 22 2012

Status

approved