login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 23:02 EDT 2021. Contains 348070 sequences. (Running on oeis4.)