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%I #10 Apr 03 2020 12:05:44
%S 1,1,1,2,3,6,9,14,22,31,46,59,89,114,158,201,281,337,472,570,756,936,
%T 1233,1456,1926,2323,2942,3556,4537,5334,6812,8088,10021,11997,14805,
%U 17432,21601,25507,30971,36606,44543,52106,63219,74097,88680,104281,124708,145205,173429,202124
%N a(n) = Sum_{d|n} (-1)^omega(n/d) * phi(rad(n/d)) * p(d), where p = A000041 (partition numbers).
%F a(n) = Sum_{d|n} A023900(n/d) * A000041(d).
%F a(n) = Sum_{d|n} A047968(n/d) * mu(d) * d.
%F Sum_{k=1..n} a(gcd(n,k)) = A000041(n).
%t Table[Sum[(-1)^PrimeNu[n/d] EulerPhi[Last[Select[Divisors[n/d], SquareFreeQ]]] PartitionsP[d], {d, Divisors[n]}], {n, 50}]
%o (PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
%o a(n) = sumdiv(n, d, (-1)^omega(n/d) * eulerphi(rad(n/d)) * numbpart(d)); \\ _Michel Marcus_, Apr 03 2020
%Y Cf. A000010, A000041, A001221, A007947, A008683, A023900, A047968, A078392.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Apr 02 2020
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