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

1,1

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)

Links

Table of n, a(n) for n=1..40.

Example

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.

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 *)

Crossrefs

Cf. A073606, A226295.

Sequence in context: A073413 A046681 A259672 * A166968 A075644 A088825

Adjacent sequences: A163616 A163617 A163618 * A163620 A163621 A163622

Keyword

nonn

Author

Leroy Quet, Aug 01 2009

Extensions

More terms from Sean A. Irvine, Oct 04 2009

Status

approved