A338894 - OEIS

%I #40 Dec 24 2020 21:27:13

%S 1,6,17,32,57,90,129,180,241,310,377,460,565,670,781,928,1053,1194,

%T 1365,1548,1705,1882,2125,2312,2561,2802,3081,3308,3565,3910,4141,

%U 4488,4849,5170,5525,5840,6237,6578,7013,7460

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

%D 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.

%H Edward Krogius, <a href="/A338894/b338894.txt">Table of n, a(n) for n = 1..1000</a>

%H Edward Krogius, <a href="/A338894/a338894.png">Illustration of 310 solutions in 100x100 grid</a>

%H YLE (Finnish Broadcasting Corporation), <a href="https://yle.fi/aihe/artikkeli/2020/02/11/2020-kevat-matematiikka-pitka-oppimaara">2020 kevät: matematiikka pitkä oppimäärä</a> (In Finnish)

%H YLE (Finnish Broadcasting Corporation), <a href="http://yle.fi/plus/abitreenit/2020/kevat/2020-03-18_M_fi/index.html">Abitreenit, Matematiikka, pitkä oppimäärä</a> (In Finnish; katso Tehtävä 12. Geometrisen keskiarvon todennäköisyyksiä, kohta 2)

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

%F a(n) = A132188(n^2). - _Antti Karttunen_, Nov 23 2020

%o (PARI) A338894(n) = sum(i=1,n*n,sum(j=1,n*n,issquare(i*j))); \\ (Naive implementation) - _Antti Karttunen_, Nov 23 2020

%Y Cf. A000010, A057918, A132188, A339026.

%K nonn

%O 1,2

%A _Edward Krogius_, Nov 14 2020