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A215950 Numbers n > 1 such that the sum of the distinct prime divisors of n^2 + 1 that are congruent to 1 mod 8 equals the sum of the distinct prime divisors congruent to 5 mod 8. 4

%I

%S 948,1560,1772,6481,13236,14191,35039,36984,40452,94536,100512,127224,

%T 154481,372377,399583,425808,623311,757382,875784,1468687,1552081,

%U 1595839,2102736,2745332,3075281,3202337,3473189,4140725,5401464,6930587,7847839,8316667

%N Numbers n > 1 such that the sum of the distinct prime divisors of n^2 + 1 that are congruent to 1 mod 8 equals the sum of the distinct prime divisors congruent to 5 mod 8.

%H Donovan Johnson, <a href="/A215950/b215950.txt">Table of n, a(n) for n = 1..100</a>

%e 948 is in the sequence because the prime distinct divisors of 948^2 + 1 are {5, 17, 97, 109} and 5+109 = 17+97 = 114, where {17, 97} == 1 mod 8 and {5, 109} == 5 mod 8.

%p with(numtheory):for n from 1 to 10^6 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:if n1>1 and s1=s3 then printf(`%d, `,n):else fi:od:

%t dpdQ[n_]:=Module[{pd=Transpose[FactorInteger[n^2+1]][[1]]},Total[ Select[ pd,Mod[ #,8] ==1&]]==Total[Select[pd,Mod[#,8]==5&]]]; Select[Range[ 2, 9*10^6],dpdQ] (* _Harvey P. Dale_, Jul 02 2016 *)

%Y Cf. A002522.

%K nonn,hard

%O 1,1

%A _Michel Lagneau_, Aug 28 2012

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Last modified December 3 17:08 EST 2021. Contains 349467 sequences. (Running on oeis4.)