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A257416 Values of n such that there are exactly 9 solutions to x^2 - y^2 = n with x > y >= 0. 3
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 (list; graph; refs; listen; history; text; internal format)
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

PROG

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

CROSSREFS

Cf. A257408-A257415, A257417.

Cf. A034178.

Sequence in context: A056457 A068351 A067892 * A137493 A179669 A067808

Adjacent sequences:  A257413 A257414 A257415 * A257417 A257418 A257419

KEYWORD

nonn

AUTHOR

Colin Barker, Apr 22 2015

STATUS

approved

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Last modified January 28 13:05 EST 2020. Contains 331321 sequences. (Running on oeis4.)