A119613 Numbers n such that the difference between the largest distinct prime divisor and the smallest distinct prime divisor is a prime.

10, 14, 15, 20, 26, 28, 30, 35, 38, 40, 42, 45, 50, 52, 56, 60, 62, 70, 75, 76, 78, 80, 84, 86, 90, 98, 100, 104, 112, 114, 120, 122, 124, 126, 130, 135, 140, 143, 146, 150, 152, 156, 160, 168, 172, 175, 180, 182, 186, 190, 196, 200, 206, 208, 210, 218, 224, 225

Offset

1,1

Comments

Obviously all terms are composite, because for primes the difference is zero. - R. J. Mathar, Feb 01 2023

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

If n = 10 then the prime divisors are 2 and 5 and the difference between these two is 3 which is also a prime. So 10 is in the sequence.
If n = 70 then the prime divisors are 2, 5 and 7 and the difference between the largest and the smallest distinct prime divisors is 5 which is also a prime. So 70 is in the sequence.

Mathematica

Select[Range[2, 300], Not[Length[FactorInteger[ # ]]==1]&&PrimeQ[FactorInteger[ # ][[ -1, 1]] -FactorInteger[ # ][[1, 1]]] &] (* Stefan Steinerberger, Jun 06 2006 *)
pQ[n_]:=Module[{fi=FactorInteger[n]}, Length[fi]>1&&PrimeQ[fi[[-1, 1]]-fi[[1, 1]]]]; Select[Range[250], pQ] (* Harvey P. Dale, Nov 19 2019 *)

Crossrefs

Sequence in context: A330136 A307589 A209800 * A154371 A172509 A036338

Adjacent sequences: A119610 A119611 A119612 * A119614 A119615 A119616

Keyword

nonn,less

Author

Parthasarathy Nambi, Jun 05 2006

Extensions

Corrected and extended by Stefan Steinerberger, Jun 06 2006

Status

approved