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A240086 a(n) = Sum_{prime p|n} phi(gcd(p, n/p)) where phi is Euler's totient function. 1

%I #18 Sep 05 2023 06:47:32

%S 0,1,1,1,1,2,1,1,2,2,1,2,1,2,2,1,1,3,1,2,2,2,1,2,4,2,2,2,1,3,1,1,2,2,

%T 2,3,1,2,2,2,1,3,1,2,3,2,1,2,6,5,2,2,1,3,2,2,2,2,1,3,1,2,3,1,2,3,1,2,

%U 2,3,1,3,1,2,5,2,2,3,1,2,2,2,1,3,2,2,2,2,1,4,2,2,2,2,2,2,1,7,3,5,1,3,1,2,3

%N a(n) = Sum_{prime p|n} phi(gcd(p, n/p)) where phi is Euler's totient function.

%H Antti Karttunen, <a href="/A240086/b240086.txt">Table of n, a(n) for n = 1..10000</a>

%F If n = p^2 for some prime p then a(n) = p - 1 and a(k) <= a(n) for k <= n. - _Peter Luschny_, Sep 05 2023

%p with(numtheory): a := n -> add(phi(igcd(d, n/d)), d = factorset(n)); seq(a(n), n=1..100);

%t a[n_] := Sum[EulerPhi[GCD[p, n/p]], {p, FactorInteger[n][[;;, 1]]}]; a[1] = 0; Array[a, 100] (* _Amiram Eldar_, Aug 29 2023 *)

%o (PARI) A240086(n) = sumdiv(n,p,(isprime(p)*eulerphi(gcd(p, n/p)))); \\ _Antti Karttunen_, Sep 23 2017

%Y Cf. A000010, A001616, A010051, A001248, A006093.

%K nonn,easy

%O 1,6

%A _Peter Luschny_, Mar 31 2014

%E More terms from _Antti Karttunen_, Sep 23 2017

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)