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A337251
Positive integers k such that k^2 = A^2+B^2+C^2 and A^3+B^3+C^3 = m^3, where gcd(A,B,C) = 1 and A, B, C, m are positive integers.
0
75, 119, 551, 755, 4501, 4895, 16371, 56863, 61091, 74201, 201797, 336709, 534793, 596827, 879397, 1007541
OFFSET
1,1
COMMENTS
From Chai Wah Wu, Sep 04 2020: (Start)
A. Martin and R. Davis showed that 91091088729334859 = sqrt(11868013975030087^2+16269106368215226^2+88837226814909894^2) is a term (see Links).
Table of values for k, A, B, C, m:
k A B C m
---------------------------------------------
75 14 23 70 71
119 3 34 114 115
551 18 349 426 493
755 145 198 714 721
4501 1016 2364 3693 4013
4895 213 3450 3466 4357
16371 3542 9286 13009 14497
56863 6213 32194 46458 51157
61091 29233 29574 44754 51985
74201 32913 38444 54264 63185
201797 106677 117252 124876 168373
336709 110051 118044 295512 306467
534793 116457 286752 436136 476393
596827 202023 234550 510270 536023
879397 43472 613560 628485 782597
1007541 272267 417416 875656 914315
(End)
LINKS
A. Martin and R. Davis, Solution of problem 143, Jahrbuch über die Fortschritte der Mathematik, Band 29, Jahrgang 1898, pub. 1900, p. 157.
EXAMPLE
56863 is in the sequence because 56863^2 = 6213^2 + 32194^2 + 46458^2, 6213^3 + 32194^3 + 46458^3 = 51157^3 and gcd(6213, 32194, 46458) = 1.
CROSSREFS
Cf. A096910.
Sequence in context: A107077 A039485 A226475 * A224477 A045196 A118225
KEYWORD
nonn,more
AUTHOR
Mo Li, Aug 21 2020
STATUS
approved