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 A216035 Squares corresponding to A215967(n). 1

%I #21 Sep 03 2012 14:10:45

%S 9,9,1,9,9,9,25,9,1,9,25,16,9,1,81,1,1,9,9,9,25,49,9,1,9,1,9,25,4,9,9,

%T 49,16,9,49,1,9,81,1,1,9,9,81,25,25,9,9,25,36,49,9,225,1,16,9,49,9,4,

%U 81,1,1,4,9,25,25,9,25,4,36,49,9,9,9,49,16,1,9

%N Squares corresponding to A215967(n).

%C This sequence gives the square equal to 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.

%C The sequence contains subsequences of consecutive squares such as {9,9}, {9,9,9}, {1,1}, {9,9,9}, ..., {121, 121}, ..., {169,169},....

%C a(A215949(n)) = 0.

%H Michel Lagneau, <a href="/A216035/b216035.txt">Table of n, a(n) for n = 1..10000</a>

%e a(35) = 49 because A215967(35) = 2365 = 5*11*43 and (11+43) - 5 = 49 is a square, where {11, 43} == 3 mod 4 and 5 ==1 mod 4.

%p with(numtheory):for n from 1 to 15000 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):y:=sqrt(x):if s1>0 and s3>0 and y=floor(y) then printf(`%d, `, x):else fi:od:

%Y Cf. A215967, A215949.

%K nonn

%O 1,1

%A _Michel Lagneau_, Aug 31 2012

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Last modified July 13 12:36 EDT 2024. Contains 374284 sequences. (Running on oeis4.)