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A215951 Numbers n such that the absolute value of the difference between the sum of the distinct prime divisors of n that are congruent to 1 mod 4 and the sum of the distinct prime divisors of n that are congruent to 3 mod 4 is a prime.

%I A215951 #11 Sep 09 2019 03:28:12
%S A215951 15,30,35,45,60,70,75,90,105,120,135,140,143,150,175,180,210,225,240,
%T A215951 245,255,270,273,280,285,286,300,315,323,350,357,360,375,385,405,420,
%U A215951 435,450,455,465,480,490,510,525,540,546,560,561,570,572,600,609,615,630
%N A215951 Numbers n such that the absolute value of the difference between the sum of the distinct prime divisors of n that are congruent to 1 mod 4 and the sum of the distinct prime divisors of n that are congruent to 3 mod 4 is a prime.
%H A215951 Amiram Eldar, <a href="/A215951/b215951.txt">Table of n, a(n) for n = 1..10000</a>
%e A215951 285 is in the sequence because 285 = 3*5*19 and (3+19) - 5 = 17 is prime, where 5 ==1 mod 4 and 3, 19 ==3 mod 4.
%p A215951 with(numtheory):for n from 2  to 1000 do:x:=factorset(n):n1:=nops(x):s1:=0:s3:=0:for m from 1 to n1 do: if irem(x[m],4)=1 then s1:=s1+x[m]:else if irem(x[m],4)=3 then s3:=s3+x[m]:else fi:fi:od:x:=abs(s1-s3):if s1>0 and s1>0 and s3>0 and type (x,prime)=true then printf(`%d, `,n):else fi:od:
%t A215951 aQ[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, (t1 = Total[Select[p, Mod[#, 4] == 1 &]]) > 0 && (t2 = Total[Select[p, Mod[#, 4] == 3 &]]) > 0 && PrimeQ@Abs[t1 - t2]]; Select[Range[630], aQ] (* _Amiram Eldar_, Sep 09 2019 *)
%Y A215951 Cf. A215947.
%K A215951 nonn
%O A215951 1,1
%A A215951 _Michel Lagneau_, Aug 28 2012