This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A194594 #18 Sep 23 2021 11:15:03 %S A194594 4,6,8,10,12,16,22,27,32,40,44,58,68,80,82,88,116,125,136,164,165,176, %T A194594 192,232,236,250,256,284,328,352,358,382,420,428,435,462,472,478,486, %U A194594 512,548,562,640,651,656,665,704,714,764,768,788,798,808,819,838 %N A194594 Numbers such that the sum of the their nonprime divisors and the sum of their prime divisors are both primes. %H A194594 Amiram Eldar, <a href="/A194594/b194594.txt">Table of n, a(n) for n = 1..10000</a> %e A194594 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 A194594 f[n_]:=Plus@@Select[Divisors[n],!PrimeQ[#]&];g[n_]:=Plus@@First/@FactorInteger[n];Select[Range[1000],PrimeQ[f[#]&&PrimeQ[g[#]]]&] %t A194594 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 A194594 (PARI) isok(n) = isprime(s=sumdiv(n, d, if (isprime(d), d))) && isprime(sigma(n)-s); \\ _Michel Marcus_, Jan 07 2020 %Y A194594 Cf. A008472, A023890, A194579, A114522. %K A194594 nonn %O A194594 1,1 %A A194594 _Michel Lagneau_, Aug 30 2011