cp's OEIS Frontend

A141807 Numbers k such that the maximal prime power divisors of k form a run of integers.

%I A141807 #22 Aug 31 2022 20:47:48
%S A141807 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,
%T A141807 49,53,56,59,60,61,64,67,71,72,73,79,81,83,89,97,101,103,107,109,113,
%U A141807 121,125,127,128,131,137,139,149,151,157,163,167,169,173,179,181,191
%N A141807 Numbers k such that the maximal prime power divisors of k form a run of integers.
%C A141807 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.
%C A141807 All prime powers (A000961) are included in this sequence.
%C A141807 Sequence A141808 consists of the terms of this sequence that are not prime powers.
%H A141807 Ivan Neretin, <a href="/A141807/b141807.txt">Table of n, a(n) for n = 1..10000</a>
%e A141807 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.
%t A141807 Select[Range[192], (pp = Sort[#[[1]]^#[[2]] & /@ FactorInteger@#]) - pp[[1]] + 1 == Range@Length@pp &] (* _Ivan Neretin_, Aug 13 2015 *)
%Y A141807 Cf. A000961, A141808, A262723.
%K A141807 nonn
%O A141807 1,2
%A A141807 _Leroy Quet_, Jul 07 2008
%E A141807 Extended by _Ray Chandler_, Jun 21 2009
%E A141807 New name from _Peter Munn_, Aug 31 2022