A338894 Number of ordered pairs (x,y): 1 <= x, y <= n*n, such that x*y is a square.

1, 6, 17, 32, 57, 90, 129, 180, 241, 310, 377, 460, 565, 670, 781, 928, 1053, 1194, 1365, 1548, 1705, 1882, 2125, 2312, 2561, 2802, 3081, 3308, 3565, 3910, 4141, 4488, 4849, 5170, 5525, 5840, 6237, 6578, 7013, 7460

Offset: 1

Author

Edward Krogius, Nov 14 2020

Keywords

• nonn

References

• The Finnish National Upper secondary Matriculation Examination Long Maths Problem #12 (Mar 18th, 2020) included finding all gridpoints in a [1..100]x[1..100] grid with an integer geometric mean sparked some national interest in gcd integer sequences and their generating algorithms.

Links

• Edward Krogius, Table of n, a(n) for n = 1..1000
• Edward Krogius, Illustration of 310 solutions in 100x100 grid
• YLE (Finnish Broadcasting Corporation), 2020 kevät: matematiikka pitkä oppimäärä (In Finnish)
• YLE (Finnish Broadcasting Corporation), Abitreenit, Matematiikka, pitkä oppimäärä (In Finnish; katso Tehtävä 12. Geometrisen keskiarvon todennäköisyyksiä, kohta 2)

Crossrefs

Cf. A000010, A057918, A132188, A339026.

Programs

PARI

A338894(n) = sum(i=1,n*n,sum(j=1,n*n,issquare(i*j))); \\ (Naive implementation) - Antti Karttunen, Nov 23 2020

Formula

a(n) = 2*A339026(n) + n^2.

a(n) = A132188(n^2). - Antti Karttunen, Nov 23 2020