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%I #16 Feb 25 2018 23:01:16
%S 0,1,1,3,1,3,1,7,4,5,1,8,1,7,6,15,1,10,1,14,8,11,1,18,6,13,13,20,1,14,
%T 1,31,12,17,10,26,1,19,14,32,1,20,1,32,22,23,1,38,8,26,18,38,1,31,14,
%U 46,20,29,1,36,1,31,30,63,16,32,1,50,24,34,1,58,1,37,32,56,16,38,1,68,40
%N a(n) = sum of j's for those k's, 1 <= k <= n, where gcd(k,n) = p^j, p = prime.
%H Antti Karttunen, <a href="/A122410/b122410.txt">Table of n, a(n) for n = 1..65537</a>
%e The positive integers k, k <= 12, where gcd(k,12) = a power of a prime, are 1, 2, 3, 4, 8, 9 and 10; gcd(1,12) = p^0, gcd(2,12) = 2^1, gcd(3,12) = 3^1, gcd(4,12) = 2^2, gcd(8,12) = 2^2, gcd(9,12) = 3^1 and gcd(10,12) = 2^1. The sum of the exponents raising the primes is 0+1+1+2+2+1+1 = 8. So a(12) = 8.
%t f[n_] := Plus @@ Last /@ Flatten[Select[FactorInteger[GCD[Range[n], n]], Length[ # ] == 1 &], 1]; Table[f[n], {n, 80}] (* _Ray Chandler_, Sep 06 2006 *)
%o (PARI) A122410(n) = sum(k=1,n,isprimepower(gcd(n,k))); \\ _Antti Karttunen_, Feb 25 2018
%Y Cf. A122411.
%K nonn
%O 1,4
%A _Leroy Quet_, Sep 02 2006
%E Extended by _Ray Chandler_, Sep 06 2006
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