OFFSET
1,2
COMMENTS
Partial sums of A076078.
LINKS
FORMULA
a(n) = Sum_{k=1..n} Sum_{d|k} mu(k/d) * (2^tau(d) - 1), where tau = A000005.
EXAMPLE
a(5) = 11 sets: {1}, {2}, {3}, {4}, {5}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 4} and {1, 2, 4}.
MATHEMATICA
Table[Sum[Sum[MoebiusMu[k/d] (2^DivisorSigma[0, d] - 1), {d, Divisors[k]}], {k, n}], {n, 55}]
Accumulate[Table[Sum[MoebiusMu[k/d] (2^DivisorSigma[0, d] - 1), {d, Divisors[k]}], {k, 1, 60}]] (* Vaclav Kotesovec, Dec 25 2020 *)
PROG
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, moebius(k/d) * (2^numdiv(d) - 1))); \\ Michel Marcus, Dec 11 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 11 2020
STATUS
approved