

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.


2



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
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OFFSET

1,1


COMMENTS

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


LINKS

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


EXAMPLE

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.


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 *)


CROSSREFS

Sequence in context: A281885 A183589 A185990 * A031838 A331664 A031826
Adjacent sequences: A215946 A215947 A215948 * A215950 A215951 A215952


KEYWORD

nonn


AUTHOR

Michel Lagneau, Aug 28 2012


STATUS

approved



