

A216035


Squares corresponding to A215967(n).


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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},....


LINKS



EXAMPLE

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.


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(s1s3):y:=sqrt(x):if s1>0 and s3>0 and y=floor(y) then printf(`%d, `, x):else fi:od:


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



