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A174940
a(n) = Sum_{d|n} A007955(d) * A008683(n/d) = Sum_{d|n} A007955(d) * mu(n/d), where A007955(m) = number of divisors of m.
1
1, 1, 2, 6, 4, 32, 6, 56, 24, 94, 10, 1686, 12, 188, 218, 960, 16, 5772, 18, 7894, 432, 472, 22, 329992, 120, 662, 702, 21750, 28, 809648, 30, 31744, 1076, 1138, 1214, 10070172, 36, 1424, 1506, 2551944, 40, 3111034, 42, 84694, 90876, 2092, 46, 254471232, 336, 124780
OFFSET
1,3
LINKS
FORMULA
Moebius transform of A007955. - Andrew Howroyd, Jan 05 2020
EXAMPLE
For n = 4, A007955(n) = b(n): a(4) = b(1)*mu(4/1) + b(2)*mu(4/2) + b(4)*mu(4/4) = 1*0 + 2*(-1) + 8*1 = 6.
MATHEMATICA
a[n_] := Sum[ MoebiusMu[n/d] * Times @@ Divisors[d], {d, Divisors[n]} ]; Table[ a[n], {n, 1, 30} ] (* Jean-François Alcover, Jan 09 2013 *)
PROG
(PARI) a(n)={sumdiv(n, d, vecprod(divisors(d))*moebius(n/d))} \\ Andrew Howroyd, Jan 05 2020
(Magma) [&+[&*Divisors(d)*MoebiusMu(n div d):d in Divisors(n)]:n in [1..50]]; // Marius A. Burtea, Jan 05 2020
CROSSREFS
Cf. A008683 (mu), A007955 (product of divisors).
Sequence in context: A108951 A181822 A346107 * A293011 A108435 A322827
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Apr 02 2010
EXTENSIONS
Terms a(31) and beyond from Andrew Howroyd, Jan 05 2020
STATUS
approved