A194594 Numbers such that the sum of the their nonprime divisors and the sum of their prime divisors are both primes.

4, 6, 8, 10, 12, 16, 22, 27, 32, 40, 44, 58, 68, 80, 82, 88, 116, 125, 136, 164, 165, 176, 192, 232, 236, 250, 256, 284, 328, 352, 358, 382, 420, 428, 435, 462, 472, 478, 486, 512, 548, 562, 640, 651, 656, 665, 704, 714, 764, 768, 788, 798, 808, 819, 838

Offset: 1

Author

Michel Lagneau, Aug 30 2011

Keywords

• nonn

Examples

			The divisors of 136 are { 1, 2, 4, 8, 17, 34, 68, 136 }, the sum of its nonprime divisors is 1 + 4 + 8 + 34 + 68 + 136 = 251 is prime, and the sum of its prime divisors is 2 + 17 = 19 is prime, hence 136 is in the sequence.
		

Links

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

Crossrefs

Cf. A008472, A023890, A194579, A114522.

Programs

Mathematica

f[n_]:=Plus@@Select[Divisors[n],!PrimeQ[#]&];g[n_]:=Plus@@First/@FactorInteger[n];Select[Range[1000],PrimeQ[f[#]&&PrimeQ[g[#]]]&]
ndpdQ[n_]:=Module[{d=Divisors[n],pr},pr=Select[d,PrimeQ];AllTrue[ {Total[ pr],Total[Complement[d,pr]]},PrimeQ]]; Select[Range[900],ndpdQ] (* Harvey P. Dale, Sep 23 2021 *)

PARI

isok(n) = isprime(s=sumdiv(n, d, if (isprime(d), d))) && isprime(sigma(n)-s); \\ Michel Marcus, Jan 07 2020