cp's OEIS Frontend

A384488 Numbers k having a divisor d such that d - k/d is prime.

%I A384488 #29 Jun 30 2025 15:43:13
%S A384488 3,4,6,8,10,12,14,15,18,20,24,26,28,30,32,35,36,38,40,42,44,48,50,54,
%T A384488 60,62,63,66,68,70,72,74,78,80,84,86,88,90,92,96,98,99,102,104,108,
%U A384488 110,114,120,122,126,128,130,132,138,140,143,144,146,150,152,154,158,162,164,168,170,174,176,180
%N A384488 Numbers k having a divisor d such that d - k/d is prime.
%C A384488 Presumably, all odd terms are in A000466.
%H A384488 Robert Israel, <a href="/A384488/b384488.txt">Table of n, a(n) for n = 1..10000</a>
%e A384488 a(6) = 12 is a term because 12 = 1*12 with 12 - 1 = 11 prime.
%p A384488 filter:= k -> ormap(d -> d^2 > k and isprime(d - k/d), numtheory:-divisors(k)):
%p A384488 select(filter, [$1..200]); # _Robert Israel_, Jun 30 2025
%t A384488 A384488Q[k_] := AnyTrue[Divisors[k], PrimeQ[# - k/#] &];
%t A384488 Select[Range[200], A384488Q] (* _Paolo Xausa_, Jun 30 2025 *)
%o A384488 (Magma) [k: k in [1..180] | not #[d: d in Divisors (k) | IsPrime(d-(k div d))] eq 0];
%o A384488 (PARI) isok(k) = fordiv(k, d, if (isprime(d - k/d), return(1))); \\ _Michel Marcus_, Jun 01 2025
%Y A384488 Cf. A000466, A005408, A355643. Includes A005563 and 2 * A052147.
%K A384488 nonn
%O A384488 1,1
%A A384488 _Juri-Stepan Gerasimov_, May 30 2025