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

1,1

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},....

a(A215949(n)) = 0.

Links

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

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

Crossrefs

Cf. A215967, A215949.

Sequence in context: A118428 A166925 A178164 * A171487 A120704 A021506

Adjacent sequences: A216032 A216033 A216034 * A216036 A216037 A216038

Keyword

nonn

Author

Michel Lagneau, Aug 31 2012

Status

approved