A257416 Values of n such that there are exactly 9 solutions to x^2 - y^2 = n with x > y >= 0.

720, 1008, 1152, 1200, 1575, 1584, 1800, 1872, 2205, 2352, 2448, 2475, 2736, 2800, 2925, 3072, 3200, 3312, 3528, 3675, 3825, 3888, 3920, 4176, 4275, 4400, 4464, 4851, 5120, 5175, 5200, 5328, 5445, 5733, 5808, 5904, 6075, 6192, 6272, 6300, 6525, 6768, 6800

Offset

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 260 terms from Colin Barker)

Example

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).

Maple

filter:= proc(n) local k;
k:= padic:-ordp(n, 2);
(k = 0 and numtheory:-tau(n)=18) or (k-1)*numtheory:-tau(n/2^k)=18
end proc:
select(filter, [$1..10^4]); # Robert Israel, Jun 19 2018

Mathematica

nn = 6800;
t = Table[0, {nn}];
Do[n = x^2 - y^2; If[n <= nn, t[[n]]++], {x, nn}, {y, 0, x - 1}];
Position[t, 9] // Flatten (* Jean-François Alcover, Jun 18 2020, after T. D. Noe in A034178 *)

Prog

(PARI) is_A257416(n)={A034178(n)==9} \\ M. F. Hasler, Apr 22 2015

Crossrefs

Cf. A257408, A257409, A257410, A257411, A257412, A257413, A257414, A257415, A257417.

Cf. A034178.

Sequence in context: A068351 A067892 A337036 * A137493 A179669 A067808

Adjacent sequences: A257413 A257414 A257415 * A257417 A257418 A257419

Keyword

nonn

Author

Colin Barker, Apr 22 2015

Status

approved