A066312 Numbers, other than prime powers, whose distinct prime factors are consecutive primes.

6, 12, 15, 18, 24, 30, 35, 36, 45, 48, 54, 60, 72, 75, 77, 90, 96, 105, 108, 120, 135, 143, 144, 150, 162, 175, 180, 192, 210, 216, 221, 225, 240, 245, 270, 288, 300, 315, 323, 324, 360, 375, 384, 385, 405, 420, 432, 437, 450, 480, 486

Offset: 1

Author

Leroy Quet, Jan 01 2002

Keywords

• nonn

Comments

Numbers whose squarefree kernel (A007947) is the product of 2 or more consecutive primes. - Peter Munn, May 27 2023

Examples

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

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A007947, A097889.

Programs

Mathematica

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

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

Formula

{a(n) : n >= 1} = {k >= 1 : A007947(k) is in A097889}. - Peter Munn, May 29 2023

Extensions

OFFSET changed from 0,1 to 1,1 by Harry J. Smith, Feb 10 2010

Name edited by Peter Munn, May 29 2023