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%I M0156 #30 Sep 25 2020 10:05:42
%S 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,
%T 59,80,60,107,41,125,78,103,79,123,66,155,95,123,90,177,75,189,110,
%U 132,115,209,100,210,114,171,134,239
%N Moebius transform of primes.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Michel Marcus, <a href="/A007444/b007444.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = Sum_{n>=1} prime(n)*x^n. - _Ilya Gutkovskiy_, Apr 25 2017
%F a(n) = Sum_{d|n} prime(d)*mu(n/d), where mu is the Moebius function (A008683). - _Wesley Ivan Hurt_, Sep 23 2020
%t a[n_] := DivisorSum[n, Prime[#] * MoebiusMu[n/#] &]; Array[a, 200] (* _Enrique Pérez Herrero_, Sep 23 2020 *)
%o (PARI) a(n) = sumdiv(n, d, prime(d)*moebius(n/d)); \\ _Michel Marcus_, Nov 04 2018
%Y Cf. A000040, A008683.
%K nonn
%O 1,1
%A _N. J. A. Sloane_.
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