A339638 Number of nonempty sets of distinct positive integers that have a least common multiple <= n.

1, 3, 5, 9, 11, 21, 23, 31, 35, 45, 47, 91, 93, 103, 113, 129, 131, 175, 177, 221, 231, 241, 243, 427, 431, 441, 449, 493, 495, 713, 715, 747, 757, 767, 777, 1177, 1179, 1189, 1199, 1383, 1385, 1603, 1605, 1649, 1693, 1703, 1705, 2457, 2461, 2505, 2515, 2559, 2561, 2745, 2755

Offset: 1

Author

Ilya Gutkovskiy, Dec 11 2020

Keywords

• nonn

Comments

Partial sums of A076078.

Examples

			a(5) = 11 sets: {1}, {2}, {3}, {4}, {5}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 4} and {1, 2, 4}.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to lcm's

Crossrefs

Cf. A000005, A076078, A100587.

Programs

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 *)

PARI

a(n) = sum(k=1, n, sumdiv(k, d, moebius(k/d) * (2^numdiv(d) - 1))); \\ Michel Marcus, Dec 11 2020

Formula

a(n) = Sum_{k=1..n} Sum_{d|k} mu(k/d) * (2^tau(d) - 1), where tau = A000005.