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A141807
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Numbers k such that the maximal prime power divisors of k form a run of integers.
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[192], (pp = Sort[#[[1]]^#[[2]] & /@ FactorInteger@#]) - pp[[1]] + 1 == Range@Length@pp &] (* Ivan Neretin, Aug 13 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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