|
%I #21 Jun 18 2020 17:03:40
%S 720,1008,1152,1200,1575,1584,1800,1872,2205,2352,2448,2475,2736,2800,
%T 2925,3072,3200,3312,3528,3675,3825,3888,3920,4176,4275,4400,4464,
%U 4851,5120,5175,5200,5328,5445,5733,5808,5904,6075,6192,6272,6300,6525,6768,6800
%N Values of n such that there are exactly 9 solutions to x^2 - y^2 = n with x > y >= 0.
%C Numbers of the following forms: p[1]*p[2]^2*p[3]^2, p[1]^2*p[2]^5, p[1]*p[2]^8, p[1]^17, 2^2*p[1]*p[2]^2*p[3]^2, 2^2*p[1]^2*p[2]^5, 2^3*p[1]^2*p[2]^2, 2^3*p[1]^8, 2^4*p[1]*p[2]^2, 2^4*p[1]^5, 2^7*p[1]^2, 2^10*p[1], 2^19, where p[i] are distinct odd primes. - _Robert Israel_, Jun 19 2018
%H Robert Israel, <a href="/A257416/b257416.txt">Table of n, a(n) for n = 1..10000</a> (first 260 terms from Colin Barker)
%e 720 is in the sequence because there are 9 solutions to x^2 - y^2 = 720, namely (x,y) = (27,3), (28,8), (29,11), (36,24), (41,31), (49,41), (63,57), (92,88), (181,179).
%p filter:= proc(n) local k;
%p k:= padic:-ordp(n,2);
%p (k = 0 and numtheory:-tau(n)=18) or (k-1)*numtheory:-tau(n/2^k)=18
%p end proc:
%p select(filter, [$1..10^4]); # _Robert Israel_, Jun 19 2018
%t nn = 6800;
%t t = Table[0, {nn}];
%t Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
%t Position[t, 9] // Flatten (* _Jean-François Alcover_, Jun 18 2020, after _T. D. Noe_ in A034178 *)
%o (PARI) is_A257416(n)={A034178(n)==9} \\ _M. F. Hasler_, Apr 22 2015
%Y Cf. A257408, A257409, A257410, A257411, A257412, A257413, A257414, A257415, A257417.
%Y Cf. A034178.
%K nonn
%O 1,1
%A _Colin Barker_, Apr 22 2015
|
