A319341 - OEIS

%I #18 Dec 21 2023 10:23:02

%S 0,0,0,1,0,0,0,3,4,0,0,2,0,0,0,7,0,4,0,4,0,0,0,6,16,0,16,6,0,0,0,15,0,

%T 0,0,10,0,0,0,12,0,0,0,10,16,0,0,14,36,16,0,12,0,16,0,18,0,0,0,8,0,0,

%U 24,31,0,0,0,16,0,0,0,22,0,0,32,18,0,0,0,28,52,0,0,12,0,0,0,30,0,16,0,22,0,0,0,30,0,36,40,36,0,0,0,36,0

%N a(n) = A000010(n) - A173557(n).

%H Antti Karttunen, <a href="/A319341/b319341.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A000010(n) - A173557(n).

%F a(n) = A318841(n) - A051953(n).

%F a(A005117(n)) = 0. - _Ivan N. Ianakiev_, Sep 18 2018

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A059956 - A307868 = 0.136246... . - _Amiram Eldar_, Dec 21 2023

%t a[n_] := EulerPhi[n] - Times @@ (FactorInteger[n][[;;, 1]] - 1); a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Dec 21 2023 *)

%o (PARI)

%o A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));

%o A319341(n) = (eulerphi(n)-A173557(n));

%Y Cf. A000010, A051953, A173557, A318841, A319340, A126864.

%Y Cf. A013661, A307868.

%K nonn,easy

%O 1,8

%A _Antti Karttunen_, Sep 17 2018