cp's OEIS Frontend

A102308 If n = product{primes p(k)|n} p(k)^b(n,p(k)), where p(k) is the k-th prime that divides n (when these primes are listed from smallest to largest) and each b(n,p(k)) is a positive integer, then the sequence contains the non-prime-powers n such that p(k)^b(n,p(k)) > p(k+1) for all k, 1<=k<= -1 + number of distinct prime divisors of n.

%I A102308 #14 Mar 11 2014 01:32:14
%S A102308 12,24,36,40,45,48,56,63,72,80,96,108,112,135,144,160,175,176,180,189,
%T A102308 192,200,208,216,224,225,252,275,288,297,320,324,325,351,352,360,384,
%U A102308 392,400,405,416,425,432,441,448,459,475,504,513,539,540,544,567,575
%N A102308 If n = product{primes p(k)|n} p(k)^b(n,p(k)), where p(k) is the k-th prime that divides n (when these primes are listed from smallest to largest) and each b(n,p(k)) is a positive integer, then the sequence contains the non-prime-powers n such that p(k)^b(n,p(k)) > p(k+1) for all k, 1<=k<= -1 + number of distinct prime divisors of n.
%e A102308 252 is factored as 2^2 * 3^2 * 7^1. Since 2^2 > 3 and 3^2 > 7, then 252 is in the sequence. On the other hand, 60 is factored as 2^2 * 3^1 * 5^1. Even though 2^2 > 3, 3^1 is not > 5. So 60 is not in the sequence.
%o A102308 (PARI) isok(n) = {my(f = factor(n)); if (#f~ == 1, return (0)); for (i=1, #f~ - 1, if (f[i, 1]^f[i, 2] <= f[i+1, 1], return (0));); return (1);} \\ _Michel Marcus_, Jan 19 2014
%Y A102308 Cf. A057715, A143907.
%K A102308 nonn
%O A102308 1,1
%A A102308 _Leroy Quet_, Sep 04 2008
%E A102308 Extended by _Ray Chandler_, Nov 06 2008