A194579 Numbers whose sum of the their nonprime divisors is prime.

4, 6, 8, 10, 12, 16, 22, 27, 28, 32, 40, 44, 46, 52, 58, 68, 80, 82, 88, 106, 112, 116, 124, 125, 136, 148, 164, 165, 166, 172, 176, 178, 192, 208, 226, 232, 236, 250, 256, 262, 284, 292, 304, 316, 328, 332, 346, 352, 358, 368, 382, 388, 420, 428, 435

Offset: 1

Author

Michel Lagneau, Aug 29 2011

Keywords

• nonn

Examples

			The divisors of 28 are {1, 2, 4, 7, 14, 28} and the sum of its nonprime divisors is 1 + 4 + 14 + 28 = 47 is prime, hence 28 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A194594.

Programs

Maple

with(numtheory): for n from 1 to 435 do x:=divisors(n): n1:=nops(x): s:=0: for k from 1 to n1 do if not isprime(x[k]) then s:=s+x[k] fi od: if isprime(s) then printf(`%d, `, n) fi od:

Mathematica

f[n_] := Plus @@ Select[Divisors[n], ! PrimeQ[#] &]; Select[Range[435], PrimeQ[f[#]] &] (* T. D. Noe, Aug 29 2011 *)

PARI

isok(n) = isprime(sumdiv(n, d, if (!isprime(d), d))); \\ Michel Marcus, Jan 07 2020