cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A064448 #23 Dec 14 2024 14:41:18
%S A064448 1,2,9,128,625,15552,117649,8388608,129140163,2000000000,25937424601,
%T A064448 2972033482752,23298085122481,1587429546508288,29192926025390625,
%U A064448 9223372036854775808,48661191875666868481,13115469358432179191808
%N A064448 a(n) = gcd(n^n, phi(n^n)).
%H A064448 Harry J. Smith, <a href="/A064448/b064448.txt">Table of n, a(n) for n=1..100</a>
%F A064448 a(n) = gcd(A000312(n), A000010(A000312(n))).
%F A064448 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
%F A064448 a(n) = A009195(A000312(n)). - _Andrew Howroyd_, Dec 14 2024
%p A064448 f:= proc(n) local F,x;
%p A064448   F:= ifactors(n)[2];
%p A064448   mul(x[1]^(n*x[2]-1),x=F) * igcd(mul(x[1],x=F), mul(x[1]-1,x=F))
%p A064448 end proc:
%p A064448 map(f, [$1..100]); # _Robert Israel_, Jan 18 2018
%o A064448 (PARI) a(n) = { my(p=n^n); gcd(p, eulerphi(p)) } \\ _Harry J. Smith_, Sep 14 2009
%Y A064448 Cf. A000010, A000312, A009195.
%K A064448 nonn
%O A064448 1,2
%A A064448 _Labos Elemer_, Oct 02 2001