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%I #11 Sep 09 2019 03:28:19
%S 73,123,128,132,157,172,173,177,212,216,228,233,237,265,273,293,322,
%T 336,337,360,372,377,378,382,392,411,472,487,523,528,560,592,608,616,
%U 657,663,672,678,688,707,718,748,757,767,822,824,829,843,871,893,897,903
%N Numbers n such that the absolute value of the difference between the sum of the prime distinct divisors of n^2 + 1 that are congruent to 1 mod 8 and the sum of the prime distinct divisors of n^2 + 1 that are congruent to 5 mod 8 is a prime.
%H Amiram Eldar, <a href="/A215963/b215963.txt">Table of n, a(n) for n = 1..10000</a>
%e 73 is in the sequence because 73^2 + 1 = 5330 = 2*5*13*41 and 41 - (5+13) = 23 is prime, where 41 == 1 mod 8 and {5, 13}==5 mod 8.
%p with(numtheory):for n from 1 to 1000 do:x:=factorset(n^2+1):n1:=nops(x):s1:=0:s3:=0:for m from 1 to n1 do: if irem(x[m],8)=1 then s1:=s1+x[m]:else if irem(x[m],8)=5 then s3:=s3+x[m]:else fi:fi:od:x:=abs(s1-s3):if s1>0 and s3>0 and type (x,prime)=true then printf(`%d, `,n):else fi:od:
%t aQ[n_] := Module[{p = FactorInteger[n^2 + 1][[;; , 1]]}, (t1 = Total[Select[p, Mod[#, 8] == 1 &]]) > 0 && (t2 = Total[Select[p, Mod[#, 8] == 5 &]]) > 0 && PrimeQ@Abs[t1 - t2]]; Select[Range[1000], aQ] (* _Amiram Eldar_, Sep 09 2019 *)
%Y Cf. A002522, A215950.
%K nonn
%O 1,1
%A _Michel Lagneau_, Aug 29 2012
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