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%I #19 Aug 31 2022 23:06:56
%S 6,12,20,56,60,72,272,504,992,16256,65792,67100672,4295032832,
%T 17179738112,274877382656,4611686016279904256,
%U 5316911983139663489309385231907684352,383123885216472214589586756168607276261994643096338432
%N Numbers k such that the maximal prime power divisors of k form a nontrivial run of integers.
%C 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.
%C Sequence A141807 is the union of the prime powers (A000961) and this sequence.
%C 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
%e 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.
%Y Cf. A000961, A141807.
%Y Cf. A000043, A000668, A262723.
%K nonn
%O 1,1
%A _Leroy Quet_, Jul 07 2008
%E Extended by _Ray Chandler_, Jun 21 2009
%E New name from _Peter Munn_, Aug 31 2022
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