A064448 a(n) = gcd(n^n, phi(n^n)).

1, 2, 9, 128, 625, 15552, 117649, 8388608, 129140163, 2000000000, 25937424601, 2972033482752, 23298085122481, 1587429546508288, 29192926025390625, 9223372036854775808, 48661191875666868481, 13115469358432179191808

Offset: 1

Author

Labos Elemer, Oct 02 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n=1..100

Crossrefs

Cf. A000010, A000312, A009195.

Programs

Maple

f:= proc(n) local F,x;
  F:= ifactors(n)[2];
  mul(x[1]^(n*x[2]-1),x=F) * igcd(mul(x[1],x=F), mul(x[1]-1,x=F))
end proc:
map(f, [$1..100]); # Robert Israel, Jan 18 2018

PARI

a(n) = { my(p=n^n); gcd(p, eulerphi(p)) } \\ Harry J. Smith, Sep 14 2009

Formula

a(n) = gcd(A000312(n), A000010(A000312(n))).

If n = Product_j (p_j)^(e_j) is the prime factorization of n, then a(n) = Product_j p_j^(n e_j - 1) * gcd(Product_j p_j, Product_j (p_j-1)). - Robert Israel, Jan 18 2018

a(n) = A009195(A000312(n)). - Andrew Howroyd, Dec 14 2024