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.

948, 1560, 1772, 6481, 13236, 14191, 35039, 36984, 40452, 94536, 100512, 127224, 154481, 372377, 399583, 425808, 623311, 757382, 875784, 1468687, 1552081, 1595839, 2102736, 2745332, 3075281, 3202337, 3473189, 4140725, 5401464, 6930587, 7847839, 8316667

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..100

Example

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.

Maple

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:

Mathematica

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 *)

Crossrefs

Cf. A002522.

Sequence in context: A093247 A248785 A199924 * A192770 A187627 A170830

Adjacent sequences: A215947 A215948 A215949 * A215951 A215952 A215953

Keyword

nonn,hard

Author

Michel Lagneau, Aug 28 2012

Status

approved