|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|