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

1,2

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

Example

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}.

Prog

(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

Crossrefs

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

Sequence in context: A228576 A329465 A324195 * A211507 A295368 A283832

Adjacent sequences: A339660 A339661 A339662 * A339664 A339665 A339666

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 11 2020

Status

approved