OFFSET
1,1
COMMENTS
Old name and expanded definition: If p^b(n,p) is the largest power of the prime p to divide n, then the positive integer non-prime-power n is included in the sequence if p(1)^b(n,p(1)) = p(2)^b(n,p(2))+1 = p(3)^b(n,p(3))+2 = ... = p(k)^b(n, p(k))+k-1, where (p(1),p(2),p(3),...,p(k)) is some permutation of the distinct primes that divide n.
Terms with two distinct prime factors occur where either 2^m+1 or 2^m-1 is a prime power. Terms with three distinct prime factors (60, 504) occur where both 2^m+1 and 2^m-1 are prime powers. There are no terms with more than three distinct prime factors. For every Mersenne prime p (A000668), p*(p+1) is in this sequence. For every prime p in A000043, 2^p*(2^p-1) is in this sequence. - Ray Chandler, Jun 21 2009
EXAMPLE
The prime factorization of 60 is 2^2 * 3^1 * 5^1. Since 60 is not a prime power and since 5^1 = 2^2 + 1 = 3^1 + 2 (i.e., the prime powers, in some order, occur in an arithmetic progression with a difference of 1 between consecutive terms), 60 is included in the sequence.
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jul 07 2008
EXTENSIONS
Extended by Ray Chandler, Jun 21 2009
New name from Peter Munn, Aug 31 2022
STATUS
approved