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

1,1

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