This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A163619 #13 Dec 03 2024 12:25:52
%S A163619 2,8,9,20,32,98,125,128,169,464,512,729,961,1280,2048,2108,5252,8000,
%T A163619 8192,9728,15872,16807,18176,22385,32768,36992,50000,53792,59049,
%U A163619 78821,81920,97556,98125,100352,124659,131072,195129,219488,223040,307328
%N 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.
%C A163619 All terms of this sequence are in sequence A073606.
%C A163619 From _Robert Israel_, Dec 01 2024: (Start)
%C A163619 If k is a term, then so is k^j for all odd j.
%C A163619 If A226295(k) is even, then prime(k)^(A226295(k)/2) is a term. (End)
%e A163619 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.
%p A163619 filter:= n ->
%p A163619 andmap(p -> n+1 mod nextprime(p) = 0, numtheory:-factorset(n)):
%p A163619 select(filter, [$2..4*10^5]); # _Robert Israel_, Dec 01 2024
%t A163619 depQ[n_]:=With[{c=NextPrime[FactorInteger[n][[;;,1]]]},AllTrue[(n+1)/c,IntegerQ]]; Select[Range[ 2,350000],depQ] (* _Harvey P. Dale_, Jun 10 2023 *)
%Y A163619 Cf. A073606, A226295.
%K A163619 nonn
%O A163619 1,1
%A A163619 _Leroy Quet_, Aug 01 2009
%E A163619 More terms from _Sean A. Irvine_, Oct 04 2009