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 A199919 Number of distinct sums of distinct divisors of n when positive and negative divisors are allowed. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified November 28 17:53 EST 2023. Contains 367419 sequences. (Running on oeis4.)