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A141808
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Numbers k such that the maximal prime power divisors of k form a nontrivial run of integers.
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1
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6, 12, 20, 56, 60, 72, 272, 504, 992, 16256, 65792, 67100672, 4295032832, 17179738112, 274877382656, 4611686016279904256, 5316911983139663489309385231907684352, 383123885216472214589586756168607276261994643096338432
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OFFSET
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1,1
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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 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
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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 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.
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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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