A163619 Let q(p) be the smallest prime greater than the prime p. A positive integer n is included in this sequence if n+1 is divisible by q(p) for each prime p dividing n.

2, 8, 9, 20, 32, 98, 125, 128, 169, 464, 512, 729, 961, 1280, 2048, 2108, 5252, 8000, 8192, 9728, 15872, 16807, 18176, 22385, 32768, 36992, 50000, 53792, 59049, 78821, 81920, 97556, 98125, 100352, 124659, 131072, 195129, 219488, 223040, 307328

Offset: 1

Author

Leroy Quet, Aug 01 2009

Keywords

• nonn

Comments

All terms of this sequence are in sequence A073606.

From Robert Israel, Dec 01 2024: (Start)

If k is a term, then so is k^j for all odd j.

If A226295(k) is even, then prime(k)^(A226295(k)/2) is a term. (End)

Examples

			20 is divisible by the primes 2 and 5. q(2) = 3, and q(5)=7. 20+1 = 21 is divisible by both 3 and 7, so 20 is in this sequence.
		

Crossrefs

Cf. A073606, A226295.

Programs

Maple

filter:= n ->
  andmap(p -> n+1 mod nextprime(p) = 0, numtheory:-factorset(n)):
select(filter, [$2..4*10^5]); # Robert Israel, Dec 01 2024

Mathematica

depQ[n_]:=With[{c=NextPrime[FactorInteger[n][[;;,1]]]},AllTrue[(n+1)/c,IntegerQ]]; Select[Range[ 2,350000],depQ] (* Harvey P. Dale, Jun 10 2023 *)

Extensions

More terms from Sean A. Irvine, Oct 04 2009