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 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))+k-1, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All prime-powers (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 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. 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

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)