cp's OEIS Frontend

A300168 Numbers of the form n^2+1 that can be expressed as j^2+k^2, j>k>1, gcd(j,k)=1, in more ways than any smaller number of this form.

%I A300168 #31 Dec 31 2019 09:27:50
%S A300168 65,2210,58565,4678570,442765765,5279766245,2419804247185,
%T A300168 271780381692170,28579081466859170,4069607103295265285
%N A300168 Numbers of the form n^2+1 that can be expressed as j^2+k^2, j>k>1, gcd(j,k)=1, in more ways than any smaller number of this form.
%C A300168 All ten known terms are squarefree. - _Ray Chandler_, Dec 31 2019
%C A300168 a(11) <= 1035219700200622531985 which is squarefree and expressible in 2047 ways. - _Ray Chandler_, Dec 24 2019
%C A300168 a(12) <= 4431331071224333359263505 which is squarefree and expressible in 4095 ways. - _Ray Chandler_, Dec 25 2019
%e A300168 a(1) = 65 = 8^2 + 1 is the smallest expressible number (65 = 7^2 + 4^2),
%e A300168 a(2) = 2210 is expressible in 3 ways (2210 = 43^2 + 19^2 = 41^2 + 23^2 = 37^2 + 29^2),
%e A300168 a(3) = 58565 is expressible in 7 ways,
%e A300168 a(4) = 4678570 is expressible in 15 ways,
%e A300168 a(5) = 442765765 is expressible in 31 ways.
%e A300168 Would a(6) be expressible in 63 ways?
%e A300168 Yes, a(6) = 5279766245 is expressible in 63 ways. - _Hugo Pfoertner_, Mar 02 2018
%e A300168 a(7) = 2419804247185 can be expressed in 127 ways.  This continues the progression that a(n) can be expressed in n^2-1 ways. - _Robert Price_, Mar 11 2018, updated by _Ray Chandler_, Dec 23 2019
%e A300168 a(8) = 271780381692170 can be expressed in 255 ways.
%e A300168 a(9) = 28579081466859170 can be expressed in 511 ways.
%e A300168 a(10) = 4069607103295265285 can be expressed in 1023 ways.
%Y A300168 Cf. A300162, A300166, A300167.
%K A300168 nonn,more,hard
%O A300168 1,1
%A A300168 _Hugo Pfoertner_, Feb 27 2018
%E A300168 a(7) from _Robert Price_, Mar 11 2018
%E A300168 a(7) corrected, a(8)-a(9) added by _Ray Chandler_, Dec 23 2019
%E A300168 a(10) added by _Ray Chandler_, Dec 31 2019