A339663 Number of nonempty subsets of divisors of n whose average is an integer.

1, 2, 3, 4, 3, 9, 3, 7, 6, 6, 3, 24, 3, 7, 13, 12, 3, 27, 3, 22, 11, 7, 3, 72, 6, 6, 12, 21, 3, 83, 3, 20, 13, 6, 11, 133, 3, 7, 11, 70, 3, 82, 3, 21, 38, 7, 3, 230, 7, 14, 13, 23, 3, 88, 11, 65, 11, 6, 3, 763, 3, 7, 35, 36, 11, 84, 3, 22, 13, 73, 3, 780, 3, 6, 37, 20, 11, 82, 3, 228

Offset: 1

Author

Ilya Gutkovskiy, Dec 11 2020

Keywords

• nonn

Examples

			a(16) = 12 subsets: {1}, {2}, {4}, {8}, {16}, {2, 4}, {2, 8}, {2, 16}, {4, 8}, {4, 16}, {8, 16} and {1, 4, 16}.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1079
• Eric Weisstein's World of Mathematics, Arithmetic Mean
• Index entries for sequences related to divisors of numbers

Crossrefs

Cf. A027750, A051293, A100587, A339664, A339665, A339666.

Programs

PARI

sumbybits(v,b) = { my(s=0,i=1); while(b>0,s += (b%2)*v[i]; i++; b >>= 1); (s); };
A339663(n) = { my(ds=divisors(n), u=#ds); sum(m=1, (2^u)-1, !(sumbybits(ds,m)%hammingweight(m))); }; \\ Antti Karttunen, Dec 12 2021