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
Examples
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.
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
Programs
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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 *) -
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
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PARI
See PARI-link \\ David A. Corneth, May 20 2021
Formula
a(p) = 9 for odd primes p. - Antti Karttunen, May 19 2021