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A141808 Numbers k such that the maximal prime power divisors of k form a nontrivial run of integers. 1
6, 12, 20, 56, 60, 72, 272, 504, 992, 16256, 65792, 67100672, 4295032832, 17179738112, 274877382656, 4611686016279904256, 5316911983139663489309385231907684352, 383123885216472214589586756168607276261994643096338432 (list; graph; refs; listen; history; text; internal format)
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.
Sequence A141807 is the union of the prime powers (A000961) and this sequence.
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
LINKS
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
Sequence in context: A220211 A028611 A220470 * A144187 A303481 A247256
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

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)