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A240086
a(n) = Sum_{prime p|n} phi(gcd(p, n/p)) where phi is Euler's totient function.
1
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, 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, 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
OFFSET
1,6
LINKS
FORMULA
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
MAPLE
with(numtheory): a := n -> add(phi(igcd(d, n/d)), d = factorset(n)); seq(a(n), n=1..100);
MATHEMATICA
a[n_] := Sum[EulerPhi[GCD[p, n/p]], {p, FactorInteger[n][[;; , 1]]}]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)
PROG
(PARI) A240086(n) = sumdiv(n, p, (isprime(p)*eulerphi(gcd(p, n/p)))); \\ Antti Karttunen, Sep 23 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Mar 31 2014
EXTENSIONS
More terms from Antti Karttunen, Sep 23 2017
STATUS
approved