A215963 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.

73, 123, 128, 132, 157, 172, 173, 177, 212, 216, 228, 233, 237, 265, 273, 293, 322, 336, 337, 360, 372, 377, 378, 382, 392, 411, 472, 487, 523, 528, 560, 592, 608, 616, 657, 663, 672, 678, 688, 707, 718, 748, 757, 767, 822, 824, 829, 843, 871, 893, 897, 903

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Maple

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:

Mathematica

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 *)

Crossrefs

Cf. A002522, A215950.

Sequence in context: A144050 A087878 A142196 * A141991 A140742 A142929

Adjacent sequences: A215960 A215961 A215962 * A215964 A215965 A215966

Keyword

nonn

Author

Michel Lagneau, Aug 29 2012

Status

approved