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%I #17 Jan 07 2020 09:07:47
%S 4,6,8,10,12,16,22,27,28,32,40,44,46,52,58,68,80,82,88,106,112,116,
%T 124,125,136,148,164,165,166,172,176,178,192,208,226,232,236,250,256,
%U 262,284,292,304,316,328,332,346,352,358,368,382,388,420,428,435
%N Numbers whose sum of the their nonprime divisors is prime.
%H Amiram Eldar, <a href="/A194579/b194579.txt">Table of n, a(n) for n = 1..10000</a>
%e The divisors of 28 are {1, 2, 4, 7, 14, 28} and the sum of its nonprime divisors is 1 + 4 + 14 + 28 = 47 is prime, hence 28 is in the sequence.
%p with(numtheory): for n from 1 to 435 do x:=divisors(n): n1:=nops(x): s:=0: for k from 1 to n1 do if not isprime(x[k]) then s:=s+x[k] fi od: if isprime(s) then printf(`%d, `, n) fi od:
%t f[n_] := Plus @@ Select[Divisors[n], ! PrimeQ[#] &]; Select[Range[435], PrimeQ[f[#]] &] (* _T. D. Noe_, Aug 29 2011 *)
%o (PARI) isok(n) = isprime(sumdiv(n, d, if (!isprime(d), d))); \\ _Michel Marcus_, Jan 07 2020
%Y Cf. A194594.
%K nonn
%O 1,1
%A _Michel Lagneau_, Aug 29 2011
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