A333178 - OEIS

%I #6 Mar 10 2020 10:29:05

%S 2,5,7,9,13,23,19,21,25,45,33,51,43,65,65,55,61,89,69,91,97,115,85,

%T 115,99,147,105,133,111,223,129,133,175,203,179,183,159,235,215,205,

%U 181,337,193,233,233,287,213,283,229,331,299,289,243,359,301,301,343,385,279,461

%N a(n) = Sum_{d|n, gcd(d, n/d) = 1} prime(d).

%F Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * a(d) = prime(n).

%t a[n_] := Sum[If[GCD[n/d, d] == 1, Prime[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 60}]

%o (PARI) a(n) = sumdiv(n, d, if (gcd(d, n/d) ==1, prime(d))); \\ _Michel Marcus_, Mar 10 2020

%Y Cf. A000040, A001221, A007445, A076479, A333177.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Mar 10 2020