A292714 - OEIS

%I #17 Dec 05 2024 09:26:51

%S 2197,4934,5386,7606,10774,11434,15212,15214,15634,16294,17146,18134,

%T 18374,18994,19466,20134,20362,23194,23451,24051,24874,25526,25934,

%U 26326,27411,27561,27994,28486,28561,30034,31334,31366,36748,37834,38074,40694,44054,46234,47494,49834

%N Composite numbers k such that phi(x) = psi(k)*phi(k) has no solution.

%C Or composite numbers k such that A007434(k) is not a totient number (A002202).

%C Prime power terms are 13^3, 13^4, 353^2, 457^2, 733^2, 877^2, 997^2, ...

%H Amiram Eldar, <a href="/A292714/b292714.txt">Table of n, a(n) for n = 1..10000</a>

%e 4934 = 2*2467 is a term because psi(4934)*phi(4934) = (2^2 - 1)*(2467^2 - 1) = 2^3*3^3*137*617 is not a totient number (A002202).

%o (PARI) is(k) = if(isprime(k), 0, my(f = factor(k)); !istotient(prod(i = 1, #f~, (f[i, 1]^2 - 1) * f[i, 1]^(2*f[i, 2] - 2)))); \\ _Amiram Eldar_, Dec 05 2024

%Y Cf. A000010, A001615, A002202, A007434, A281958.

%K nonn

%O 1,1

%A _Altug Alkan_, Sep 21 2017