%I #23 Jun 02 2023 01:59:22

%S 6,12,15,18,24,30,35,36,45,48,54,60,72,75,77,90,96,105,108,120,135,

%T 143,144,150,162,175,180,192,210,216,221,225,240,245,270,288,300,315,

%U 323,324,360,375,384,385,405,420,432,437,450,480,486

%N Numbers, other than prime powers, whose distinct prime factors are consecutive primes.

%C Numbers whose squarefree kernel (A007947) is the product of 2 or more consecutive primes. - _Peter Munn_, May 27 2023

%H Harry J. Smith, <a href="/A066312/b066312.txt">Table of n, a(n) for n=1..1000</a>

%F {a(n) : n >= 1} = {k >= 1 : A007947(k) is in A097889}. - _Peter Munn_, May 29 2023

%e 75 is included because 75 = 3 * 5^2 and 3 and 5 are consecutive primes.

%t Select[Range[2, 500], And[! PrimePowerQ@ #, Union@ Differences@ PrimePi[FactorInteger[#][[All, 1]]] == {1}] &] (* _Michael De Vlieger_, Sep 24 2017 *)

%o (PARI) { n=0; for (m=2, 10^9, f=factor(m); b=1; if (matsize(f)[1] == 1, next); for (i=2, matsize(f)[1], if (primepi(f[i, 1]) - primepi(f[i - 1, 1]) > 1, b=0; break)); if (b, write("b066312.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 10 2010

%Y Cf. A007947, A097889.

%K nonn

%O 1,1

%A _Leroy Quet_, Jan 01 2002

%E OFFSET changed from 0,1 to 1,1 by _Harry J. Smith_, Feb 10 2010

%E Name edited by _Peter Munn_, May 29 2023