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A092509 Möbius transform of sequence A008475.

%I A092509 #14 Nov 17 2017 20:32:23
%S A092509 0,2,3,2,5,0,7,4,6,0,11,0,13,0,0,8,17,0,19,0,0,0,23,0,20,0,18,0,29,0,
%T A092509 31,16,0,0,0,0,37,0,0,0,41,0,43,0,0,0,47,0,42,0,0,0,53,0,0,0,0,0,59,0,
%U A092509 61,0,0,32,0,0,67,0,0,0,71,0,73,0,0,0,0,0,79,0,54,0,83,0,0,0,0,0,89,0,0,0,0
%N A092509 Möbius transform of sequence A008475.
%H A092509 Antti Karttunen, <a href="/A092509/b092509.txt">Table of n, a(n) for n = 1..16384</a>
%F A092509 a(n) = 0 if n is 1 or not a power of a prime;
%F A092509 a(n) = n if n is a prime;
%F A092509 a(n) = n*(1 -1/p) if n = p^k, k>= 2, p=prime.
%F A092509 a(n) = Sum_{d|n} A008683(d)*A008475(n/d). - _Antti Karttunen_, Nov 17 2017
%t A092509 f[n_] := Plus @@ Map[Power @@ #1 &, FactorInteger[n]]; mt[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*f /@ d)]; Table[ mt[n], {n, 93}] (* _Robert G. Wilson v_, Jan 12 2005 *)
%o A092509 (PARI)
%o A092509 A008475(n) = { my(f=factor(n)); vecsum(vector(#f~,i,f[i,1]^f[i,2])); };
%o A092509 A092509(n) = sumdiv(n,d,moebius(d)*A008475(n/d)); \\ _Antti Karttunen_, Nov 17 2017
%Y A092509 Cf. A008475, A008683.
%K A092509 nonn
%O A092509 1,2
%A A092509 _Leroy Quet_, Dec 31 2004
%E A092509 More terms from _Robert G. Wilson v_, Jan 13 2005