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A342544
a(n) = Sum_{k=1..n} phi(gcd(k, n))^(gcd(k, n) - 1).
4
1, 2, 6, 11, 260, 40, 46662, 16398, 1679630, 262408, 10000000010, 4194366, 8916100448268, 13060740684, 4398046511640, 35184372105244, 18446744073709551632, 16926661124436, 39346408075296537575442, 144115188076118572, 3833759992447475215524, 1000000000010000000020
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} phi(n/d) * phi(d)^(d-1).
If p is prime, a(p) = p-1 + (p-1)^(p-1).
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(# - 1) &]; Array[a, 20] (* Amiram Eldar, Mar 15 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, eulerphi(gcd(k, n))^(gcd(k, n)-1));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^(d-1));
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 15 2021
STATUS
approved