A066311 All distinct primes dividing n are consecutive.

2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 23, 24, 25, 27, 29, 30, 31, 32, 35, 36, 37, 41, 43, 45, 47, 48, 49, 53, 54, 59, 60, 61, 64, 67, 71, 72, 73, 75, 77, 79, 81, 83, 89, 90, 96, 97, 101, 103, 105, 107, 108, 109, 113, 120, 121, 125, 127, 128, 131, 135, 137

Offset: 1

Author

Leroy Quet, Jan 01 2002

Keywords

• nonn

Comments

If n is a term, any power of n is also a term. Also all primes are terms. - Zak Seidov, Jun 25 2015

Examples

			35 is included because 35 = 5 * 7 and 5 and 7 are consecutive primes.
		

Links

• Harry J. Smith and Robert Israel, Table of n, a(n) for n = 1..10000 (1..1000 from Harry J. Smith)

Crossrefs

Cf. A066312 (a subsequence).

Programs

Maple

select((numtheory:-pi @ max - numtheory:-pi @ min - nops) @ numtheory:-factorset = -1, [$2..1000]); # Robert Israel, Jun 25 2015

Mathematica

fi[n_]:=FactorInteger[n];Select[Range[2,5903],PrimeQ[#]||Length[fi[#]] < 2 ||Union[Differences[PrimePi[#[[1]]&/@fi[#]]]]=={1}&]
(* For first 1000 terms. - Zak Seidov, Jun 25 2015 *)

PARI

{ n=0; for (m=2, 10^9, f=factor(m); b=1; for (i=2, matsize(f)[1], if (primepi(f[i, 1]) - primepi(f[i - 1, 1]) > 1, b=0; break)); if (b, write("b066311.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 10 2010

Extensions

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