OFFSET
1,2
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 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.
All prime powers (A000961) are included in this sequence.
Sequence A141808 consists of the terms of this sequence that are not prime powers.
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
EXAMPLE
The prime factorization of 60 is 2^2 * 3^1 * 5^1. 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), then 60 is included in the sequence.
MATHEMATICA
Select[Range[192], (pp = Sort[#[[1]]^#[[2]] & /@ FactorInteger@#]) - pp[[1]] + 1 == Range@Length@pp &] (* Ivan Neretin, Aug 13 2015 *)
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