OFFSET
1,1
COMMENTS
The order of the exponents in the prime factorization is not significant (compare A091405).
Conjecture: (1) The sequence is infinite. (2) For every prime signature other than perfect powers, there exists a number k such that k+1 also has the same prime signature.
Up to at least 3*10^8, all numbers in this sequence have signatures with some prime to power 1 (for example, p^2*q^3 does not appear), casting some doubt on the second conjecture. - Joseph Myers, Feb 24 2004
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..112
EXAMPLE
2 and 3 both are prime, 14 and 15 both are of the type p*q and 44 and 45 both are of the prime signature p^2*q. All prime signatures occur only once.
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 14 2003
EXTENSIONS
More terms from Joseph Myers, Feb 24 2004
Offset corrected by Amiram Eldar, Jul 23 2021
STATUS
approved