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.

1, 6, 10, 14, 15, 21, 22, 24, 26, 30, 33, 34, 35, 36, 38, 39, 40, 42, 46, 51, 54, 55, 56, 57, 58, 62, 65, 66, 69, 70, 74, 77, 78, 82, 85, 86, 87, 88, 91, 93, 94, 95, 100, 102, 104, 105, 106, 110, 111, 114, 115, 118, 119, 122, 123, 129, 130, 133, 134, 135, 136, 138, 141

Offset: 1

Author

Benoit Cloitre, Jan 30 2002

Keywords

• nonn

Comments

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.)

Programs

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

Extensions

Edited by Dean Hickerson, Jun 18 2002