

A141808


If p^b(n,p) is the largest power of the prime p to divide n, then the positive integer nonprimepower 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))+k1, where (p(1),p(2),p(3),...,p(k)) is some permutation of the distinct primes that divide n.


2



6, 12, 20, 56, 60, 72, 272, 504, 992, 16256, 65792, 67100672, 4295032832, 17179738112, 274877382656, 4611686016279904256, 5316911983139663489309385231907684352, 383123885216472214589586756168607276261994643096338432
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OFFSET

1,1


COMMENTS

Sequence A141807 consists of the primepowers (A000961) and the terms of A141808 together.
Terms with two distinct prime factors occur where either 2^m+1 or 2^m1 is a prime power. Terms with three distinct prime factors (60, 504) occur where both 2^m+1 and 2^m1 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^p1) is in this sequence. Chandler


LINKS

Table of n, a(n) for n=1..18.


EXAMPLE

The primefactorization 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 (ie, 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.


CROSSREFS

Cf. A141807.
Sequence in context: A220211 A028611 A220470 * A144187 A303481 A247256
Adjacent sequences: A141805 A141806 A141807 * A141809 A141810 A141811


KEYWORD

nonn


AUTHOR

Leroy Quet, Jul 07 2008


EXTENSIONS

Extended by Ray Chandler, Jun 21 2009


STATUS

approved



