

A351863


Numbers k with at least one divisor, d, such that kd is prime.


1



3, 4, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 30, 32, 34, 38, 42, 44, 46, 48, 54, 58, 60, 62, 68, 72, 74, 80, 82, 84, 86, 90, 94, 98, 102, 104, 106, 108, 110, 114, 118, 122, 128, 132, 134, 138, 140, 142, 146, 150, 152, 158, 164, 166, 168, 174, 178, 180, 182, 192, 194, 198, 200, 202
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS



FORMULA



EXAMPLE

4 is in the sequence since 4(1)=3, 4(2)=2, 4(4)=0, and at least one of 3,2,0 is prime.
56 is not in the sequence since the divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, and none of 561, 562, 564, ... etc. are prime (i.e., none of 55, 54, 52, 49, 48, 42, 28, 0 are prime).


MATHEMATICA

q[n_] := AnyTrue[Divisors[n], PrimeQ[n  #] &]; Select[Range[200], q] (* Amiram Eldar, Feb 22 2022 *)


PROG

(PARI) isok(k) = sumdiv(k, d, isprime(kd)) >= 1; \\ Michel Marcus, Feb 22 2022
(PARI) is(n) = isprime(n1)  (n%2 == 0 && isprime(n/2)) \\ David A. Corneth, Feb 22 2022
(Python)
from sympy import divisors, isprime
def ok(n): return any(isprime(nd) for d in divisors(n))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



