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A339638 Number of nonempty sets of distinct positive integers that have a least common multiple <= n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of A076078.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Index entries for sequences related to lcm's

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

Cf. A000005, A076078, A100587.

Sequence in context: A070639 A078392 A187753 * A231716 A113488 A092917

Adjacent sequences:  A339635 A339636 A339637 * A339639 A339640 A339641

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 11 2020

STATUS

approved

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Last modified January 17 23:59 EST 2021. Contains 340249 sequences. (Running on oeis4.)