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%I #18 Sep 23 2021 11:15:03
%S 4,6,8,10,12,16,22,27,32,40,44,58,68,80,82,88,116,125,136,164,165,176,
%T 192,232,236,250,256,284,328,352,358,382,420,428,435,462,472,478,486,
%U 512,548,562,640,651,656,665,704,714,764,768,788,798,808,819,838
%N Numbers such that the sum of the their nonprime divisors and the sum of their prime divisors are both primes.
%H Amiram Eldar, <a href="/A194594/b194594.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t f[n_]:=Plus@@Select[Divisors[n],!PrimeQ[#]&];g[n_]:=Plus@@First/@FactorInteger[n];Select[Range[1000],PrimeQ[f[#]&&PrimeQ[g[#]]]&]
%t 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 *)
%o (PARI) isok(n) = isprime(s=sumdiv(n, d, if (isprime(d), d))) && isprime(sigma(n)-s); \\ _Michel Marcus_, Jan 07 2020
%Y Cf. A008472, A023890, A194579, A114522.
%K nonn
%O 1,1
%A _Michel Lagneau_, Aug 30 2011
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