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A097101 Numbers n that are the hypotenuse of exactly 7 distinct integer-sided right triangles, i.e., n^2 can be written as a sum of two squares in 7 ways. 24
325, 425, 650, 725, 845, 850, 925, 975, 1025, 1275, 1300, 1325, 1445, 1450, 1525, 1690, 1700, 1825, 1850, 1950, 2050, 2175, 2225, 2275, 2425, 2525, 2535, 2550, 2600, 2650, 2725, 2775, 2825, 2873, 2890, 2900, 2925, 2975 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Comment from R. J. Mathar, Feb 26 2008, edited by Zak Seidov May 12 2008: (Start)

There are nonsquares x which can be written as a sum of 2 nonzero squares in exactly 7 different ways and which are by definition not in this sequence.

203125 = (125*sqrt(13))^2 is the first example: 203125 = 625 + 202500 = 10404 + 192721 = 18225 + 184900= 22500 + 180625= 62500 + 140625= 69169 + 133956= 84100 + 119025.

The second and third examples are 265625 = (125*sqrt(17))^2 and 406250=(125*sqrt(26))^2. (End)

If m is a term, then 2*m and p*m are terms where p is any prime of the form 4k+3. - Ray Chandler, Dec 30 2019

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

FORMULA

Equals {n: A025426(n^2)=7}.

EXAMPLE

Example supplied by R. J. Mathar, Feb 26 2008:

The smallest number that can be written as a sum of two nonzero squares in 7 different ways is 105625 = 325^2:

1296 + 104329 = 105625 = 325^2

6400 + 99225 = 105625 = 325^2

8281 + 97344 = 105625 = 325^2

15625 + 90000 = 105625 = 325^2

27225 + 78400 = 105625 = 325^2

38025 + 67600 = 105625 = 325^2

41616 + 64009 = 105625 = 325^2.

MATHEMATICA

r[a_]:={b, c}/.{ToRules[Reduce[0<b<c && a^2 == b^2 + c^2, {b, c}, Integers]]}; Select[Range[3000], Length[r[#]] == 7 &] (* Vincenzo Librandi, Mar 01 2016 *)

CROSSREFS

Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A290499 (8), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).

Sequence in context: A184036 A159844 A000443 * A025294 A025313 A025286

Adjacent sequences:  A097098 A097099 A097100 * A097102 A097103 A097104

KEYWORD

nonn

AUTHOR

James R. Buddenhagen, Sep 15 2004

EXTENSIONS

Definition and comments corrected by Zak Seidov, Feb 26 2008, May 12 2008

STATUS

approved

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Last modified January 19 12:48 EST 2020. Contains 331049 sequences. (Running on oeis4.)