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A141807
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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.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| All prime-powers (A000961) are included in this sequence.
Sequence A141808 consists of terms of A141807 that are not prime powers.
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EXAMPLE
| The prime-factorization 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.
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CROSSREFS
| Cf. A141808.
Sequence in context: A055201 A072303 A081061 * A072495 A126968 A126969
Adjacent sequences: A141804 A141805 A141806 * A141808 A141809 A141810
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Jul 07 2008
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 21 2009
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