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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. 0
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

Table of n, a(n) for n=1..55.

EXAMPLE

The divisors of 136  are  { 1, 2, 4, 8, 17, 34, 68, 136 } ;  the sum of the nonprime divisors  1+4+8+34+68+136 = 251  is prime, the sum of the prime divisors  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[#]]]&]

CROSSREFS

Cf. A008472, A023890, A194579, A114522.

Sequence in context: A310659 A076298 A194579 * A163248 A034288 A131984

Adjacent sequences:  A194591 A194592 A194593 * A194595 A194596 A194597

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 30 2011

STATUS

approved

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Last modified April 24 04:23 EDT 2019. Contains 322406 sequences. (Running on oeis4.)