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.

15, 30, 35, 45, 60, 70, 75, 90, 105, 120, 135, 140, 143, 150, 175, 180, 210, 225, 240, 245, 255, 270, 273, 280, 285, 286, 300, 315, 323, 350, 357, 360, 375, 385, 405, 420, 435, 450, 455, 465, 480, 490, 510, 525, 540, 546, 560, 561, 570, 572, 600, 609, 615, 630

Offset

1,1

Links

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

Example

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.

Maple

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:

Mathematica

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 *)

Crossrefs

Cf. A215947.

Sequence in context: A239247 A291045 A079877 * A060700 A167210 A131933

Adjacent sequences: A215948 A215949 A215950 * A215952 A215953 A215954

Keyword

nonn

Author

Michel Lagneau, Aug 28 2012

Status

approved