A216035 Squares corresponding to A215967(n).

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

Offset: 1

Author

Michel Lagneau, Aug 31 2012

Keywords

• nonn

Comments

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.

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

a(A215949(n)) = 0.

Examples

			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.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A215967, A215949.

Programs

Maple

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: