A328151 a(n) is the smallest nonnegative integer k where exactly n ordered pairs of positive integers (x, y) exist such that x^2 + y^2 = k.

0, 2, 5, 50, 65, 1250, 325, 31250, 1105, 8450, 8125, 19531250, 5525, 488281250, 105625, 211250, 27625, 305175781250, 71825, 7629394531250, 138125, 5281250, 126953125

Offset

0,2

Comments

a(n) is the smallest nonnegative i such that A063725(i) = n.

Links

Table of n, a(n) for n=0..22.

Formula

Conjecture: a(2k) = A093195(k) for k >= 1, a(2k+1) = 2*A006339(k)^2 for k >= 0. - Jon E. Schoenfield, Jan 23 2022

Example

For n = 3: The sums of the two members of each of the pairs (1, 49), (25, 25) and (49, 1) is 50 and 50 is the smallest nonnegative integer where exactly 3 such pairs exist, so a(3) = 50.

Prog

(PARI) a063725(n) = if(n==0, return(0)); my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4==1, f[i, 2]+1, f[i, 2]%2==0 || f[i, 1]==2)) - issquare(n) \\ after Charles R Greathouse IV in A063725
a(n) = for(x=0, oo, if(a063725(x)==n, return(x)))

Crossrefs

Cf. A063725.

Sequence in context: A357246 A244014 A102011 * A208797 A004098 A356492

Adjacent sequences: A328148 A328149 A328150 * A328152 A328153 A328154

Keyword

nonn,hard,more

Author

Felix Fröhlich, Oct 05 2019

Extensions

a(13)-a(22) from Bert Dobbelaere, Oct 20 2019

Status

approved