A215949 Numbers n such that the sum of the distinct prime divisors of n that are congruent to 1 mod 4 equals the sum of the distinct prime divisors congruent to 3 mod 4.

4845, 5005, 9690, 10010, 11571, 13485, 14535, 19380, 20020, 23142, 24225, 25025, 26445, 26691, 26970, 28083, 29070, 34713, 35035, 35581, 36685, 38760, 40040, 40455, 43605, 46189, 46284, 47859, 48450, 50050, 52890, 53382, 53940, 54131, 55055, 56166, 58140

Offset: 1

Author

Michel Lagneau, Aug 28 2012

Keywords

• nonn

Comments

If n is odd and in this sequence, then n * 2^k is in the sequence for any k.

Examples

			4845 is in the sequence because the distinct prime divisors are {3, 5, 17, 19} and 5+17 = 3+19 = 22, where {5, 17} ==1 mod 4 and {3, 19} ==3 mod 4.
		

Links

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

Programs

Maple

with(numtheory):for n from 2 to 60000 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:if n1>1 and s1=s3 then printf(`%d, `,n):else fi:od:

Mathematica

aQ[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, (t = Total[Select[p, Mod[#, 4] == 1 &]]) > 0 && t == Total[Select[p, Mod[#, 4] == 3 &]]]; Select[Range[10^5], aQ] (* Amiram Eldar, Sep 09 2019 *)