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

1,2

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.)

Links

Table of n, a(n) for n=1..63.

Prog

(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

Crossrefs

Sequence in context: A066073 A339438 A268376 * A229153 A119847 A279458

Adjacent sequences: A067579 A067580 A067581 * A067583 A067584 A067585

Keyword

nonn

Author

Benoit Cloitre, Jan 30 2002

Extensions

Edited by Dean Hickerson, Jun 18 2002

Status

approved