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 A194594 Numbers such that the sum of the their nonprime divisors and the sum of their prime divisors are both primes. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 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. 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 *) PROG (PARI) isok(n) = isprime(s=sumdiv(n, d, if (isprime(d), d))) && isprime(sigma(n)-s); \\ Michel Marcus, Jan 07 2020 CROSSREFS Cf. A008472, A023890, A194579, A114522. Sequence in context: A310659 A076298 A194579 * A163248 A341280 A034288 Adjacent sequences: A194591 A194592 A194593 * A194595 A194596 A194597 KEYWORD nonn AUTHOR Michel Lagneau, Aug 30 2011 STATUS approved

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Last modified September 11 16:20 EDT 2024. Contains 375836 sequences. (Running on oeis4.)