A215949 - OEIS

%I #10 Sep 09 2019 03:28:23

%S 4845,5005,9690,10010,11571,13485,14535,19380,20020,23142,24225,25025,

%T 26445,26691,26970,28083,29070,34713,35035,35581,36685,38760,40040,

%U 40455,43605,46189,46284,47859,48450,50050,52890,53382,53940,54131,55055,56166,58140

%N 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.

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

%H Amiram Eldar, <a href="/A215949/b215949.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p 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:

%t 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 *)

%K nonn

%O 1,1

%A _Michel Lagneau_, Aug 28 2012