

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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



