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

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

Offset

1,2

Links

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

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

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

Prog

(PARI) { for (n=1, 100, p=n^n; write("b064448.txt", n, " ", gcd(p, eulerphi(p))) ) } \\ Harry J. Smith, Sep 14 2009

Crossrefs

Cf. A000010, A000312.

Sequence in context: A162955 A197314 A295331 * A173215 A110817 A189428

Adjacent sequences: A064445 A064446 A064447 * A064449 A064450 A064451

Keyword

nonn

Author

Labos Elemer, Oct 02 2001

Status

approved