|
|
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.
|
|
0
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
All terms of this sequence are in sequence A073606.
|
|
LINKS
|
|
|
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.
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|