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A344223
a(n) = Sum_{k=1..n} tau(gcd(k,n)^n), where tau(n) is the number of divisors of n.
7
1, 4, 6, 16, 10, 72, 14, 64, 45, 180, 22, 600, 26, 336, 360, 256, 34, 1620, 38, 1600, 672, 792, 46, 4752, 175, 1092, 378, 3080, 58, 36960, 62, 1024, 1584, 1836, 1680, 17136, 74, 2280, 2184, 12960, 82, 97020, 86, 7480, 9450, 3312, 94, 37536, 441, 16900, 3672, 10400, 106, 40824, 3960, 25200
OFFSET
1,2
LINKS
FORMULA
a(n) = n * A344226(n).
a(n) = Sum_{d|n} phi(n/d) * tau(d^n).
a(n) = n * Sum_{d|n} n^omega(d) / d.
If p is prime, a(p) = 2*p.
MATHEMATICA
Table[Sum[DivisorSigma[0, GCD[k, n]^n], {k, n}], {n, 100}] (* Giorgos Kalogeropoulos, May 13 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n)^n));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d^n));
(PARI) a(n) = n*sumdiv(n, d, n^omega(d)/d);
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 12 2021
STATUS
approved