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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A066312 (a subsequence).

Sequence in context: A362981 A193671 A073491 * A069899 A081306 A130073

Adjacent sequences: A066308 A066309 A066310 * A066312 A066313 A066314

Keyword

nonn

Author

Leroy Quet, Jan 01 2002

Extensions

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

Status

approved