A007444 Moebius transform of primes.

2, 1, 3, 4, 9, 7, 15, 12, 18, 17, 29, 20, 39, 25, 33, 34, 57, 30, 65, 38, 53, 47, 81, 40, 86, 59, 80, 60, 107, 41, 125, 78, 103, 79, 123, 66, 155, 95, 123, 90, 177, 75, 189, 110, 132, 115, 209, 100, 210, 114, 171, 134, 239

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000040, A008683.

Programs

Mathematica

a[n_] := DivisorSum[n, Prime[#] * MoebiusMu[n/#] &]; Array[a, 200] (* Enrique Pérez Herrero, Sep 23 2020 *)

PARI

a(n) = sumdiv(n, d, prime(d)*moebius(n/d)); \\ Michel Marcus, Nov 04 2018

Formula

G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = Sum_{n>=1} prime(n)*x^n. - Ilya Gutkovskiy, Apr 25 2017

a(n) = Sum_{d|n} prime(d)*mu(n/d), where mu is the Moebius function (A008683). - Wesley Ivan Hurt, Sep 23 2020