

A141807


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))+k1, where (p(1),p(2),p(3),...,p(k)) is some permutation of the distinct primes that divide n.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 19, 20, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 56, 59, 60, 61, 64, 67, 71, 72, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191
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OFFSET

1,2


COMMENTS

All primepowers (A000961) are included in this sequence.
Sequence A141808 consists of terms of A141807 that are not prime powers.


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000


EXAMPLE

The primefactorization of 60 is 2^2 *3^1 *5^1. 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.


MATHEMATICA

Select[Range[192], (pp = Sort[#[[1]]^#[[2]] & /@ FactorInteger@#])  pp[[1]] + 1 == Range@Length@pp &] (* Ivan Neretin, Aug 13 2015 *)


CROSSREFS

Cf. A141808.
Sequence in context: A243068 A081061 A317589 * A246422 A072495 A257671
Adjacent sequences: A141804 A141805 A141806 * A141808 A141809 A141810


KEYWORD

nonn


AUTHOR

Leroy Quet, Jul 07 2008


EXTENSIONS

Extended by Ray Chandler, Jun 21 2009


STATUS

approved



