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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

%I

%S 4,6,8,10,12,16,22,27,32,40,44,58,68,80,82,88,116,125,136,164,165,176,

%T 192,232,236,250,256,284,328,352,358,382,420,428,435,462,472,478,486,

%U 512,548,562,640,651,656,665,704,714,764,768,788,798,808,819,838

%N Numbers such that the sum of the their nonprime divisors and the sum of their prime divisors are both primes.

%e 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.

%t f[n_]:=Plus@@Select[Divisors[n],!PrimeQ[#]&];g[n_]:=Plus@@First/@FactorInteger[n];Select[Range[1000],PrimeQ[f[#]&&PrimeQ[g[#]]]&]

%Y Cf. A008472, A023890, A194579, A114522.

%K nonn

%O 1,1

%A _Michel Lagneau_, Aug 30 2011

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Last modified May 21 15:02 EDT 2019. Contains 323443 sequences. (Running on oeis4.)