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A361707 Moebius transform applied twice to primes.

%I A361707 #16 Apr 02 2023 12:38:34
%S A361707 2,-1,1,3,7,5,13,8,15,9,27,10,37,11,23,22,55,8,63,18,37,19,79,12,77,
%T A361707 21,62,32,105,-5,123,44,73,23,101,23,153,31,83,44,175,7,187,60,84,35,
%U A361707 207,38,195,20,113,72,237,18,181,76,133,55,273,34,279,41,148,102,217
%N A361707 Moebius transform applied twice to primes.
%H A361707 Winston de Greef, <a href="/A361707/b361707.txt">Table of n, a(n) for n = 1..10000</a>
%H A361707 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A361707 a(n) = Sum_{d|n} A007427(n/d) * prime(d).
%p A361707 a:= (proc(p) proc(n) uses numtheory;
%p A361707        add(p(d)*mobius(n/d), d=divisors(n))
%p A361707      end end@@2)(ithprime):
%p A361707 seq(a(n), n=1..100);  # _Alois P. Heinz_, Mar 23 2023
%t A361707 A007427[n_] := Sum[MoebiusMu[n/d] MoebiusMu[d], {d, Divisors[n]}]; a[n_] := Sum[A007427[n/d] Prime[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 65}]
%o A361707 (PARI) A007427(n) = if( n<1, 0, direuler(p=2, n, (1 - 'x)^2)[n]) \\ from _Michael Somos_, Nov 15 2002
%o A361707 A361707(n)=sumdiv(n, d, A007427(n/d) * prime(d)) \\ _Winston de Greef_, Mar 23 2023
%Y A361707 Cf. A000040, A007427, A007431, A007444, A361706.
%K A361707 sign,look
%O A361707 1,1
%A A361707 _Ilya Gutkovskiy_, Mar 21 2023