A067582 - OEIS

A067582

Nonprime values of n such that bigomega(n)^omega(n)=omega(n)^bigomega(n) where bigomega(n) is the number of prime factors of n (counted with multiplicity) and omega(n) the number of distinct prime factors of n.

%I #12 Oct 15 2015 16:38:13

%S 1,6,10,14,15,21,22,24,26,30,33,34,35,36,38,39,40,42,46,51,54,55,56,

%T 57,58,62,65,66,69,70,74,77,78,82,85,86,87,88,91,93,94,95,100,102,104,

%U 105,106,110,111,114,115,118,119,122,123,129,130,133,134,135,136,138,141

%N Nonprime values of n such that bigomega(n)^omega(n)=omega(n)^bigomega(n) where bigomega(n) is the number of prime factors of n (counted with multiplicity) and omega(n) the number of distinct prime factors of n.

%C Consists of nonprime squarefree numbers A000469(n) and numbers of the forms p*q^3 and p^2*q^2 for distinct primes p and q. (The solutions in positive integers of x^y=y^x are x=y and {x,y}={2,4}. The first case gives the squarefree numbers; the second gives the other two forms.)

%o (PARI) is(n)=my(f=factor(n)[,2],b=vecsum(f),o=#f); b!=1 && b^o==o^b \\ _Charles R Greathouse IV_, Oct 15 2015

%K nonn

%O 1,2

%A _Benoit Cloitre_, Jan 30 2002

%E Edited by _Dean Hickerson_, Jun 18 2002