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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007947, A097889.

Sequence in context: A104210 A378884 A356736 * A309944 A212308 A089341

Adjacent sequences: A066309 A066310 A066311 * A066313 A066314 A066315

Keyword

nonn

Author

Leroy Quet, Jan 01 2002

Extensions

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

Name edited by Peter Munn, May 29 2023

Status

approved