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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},....

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

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Last modified October 16 06:18 EDT 2019. Contains 328046 sequences. (Running on oeis4.)