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 A300168 Numbers of the form n^2+1 that can be expressed as j^2+k^2, j>k>1, gcd(j,k)=1, in more ways than any smaller number of this form. 5
 65, 2210, 58565, 4678570, 442765765, 5279766245, 2419804247185, 271780381692170, 28579081466859170, 4069607103295265285 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All ten known terms are squarefree. - Ray Chandler, Dec 31 2019 a(11) <= 1035219700200622531985 which is squarefree and expressible in 2047 ways. - Ray Chandler, Dec 24 2019 a(12) <= 4431331071224333359263505 which is squarefree and expressible in 4095 ways. - Ray Chandler, Dec 25 2019 LINKS Table of n, a(n) for n=1..10. EXAMPLE a(1) = 65 = 8^2 + 1 is the smallest expressible number (65 = 7^2 + 4^2), a(2) = 2210 is expressible in 3 ways (2210 = 43^2 + 19^2 = 41^2 + 23^2 = 37^2 + 29^2), a(3) = 58565 is expressible in 7 ways, a(4) = 4678570 is expressible in 15 ways, a(5) = 442765765 is expressible in 31 ways. Would a(6) be expressible in 63 ways? Yes, a(6) = 5279766245 is expressible in 63 ways. - Hugo Pfoertner, Mar 02 2018 a(7) = 2419804247185 can be expressed in 127 ways. This continues the progression that a(n) can be expressed in n^2-1 ways. - Robert Price, Mar 11 2018, updated by Ray Chandler, Dec 23 2019 a(8) = 271780381692170 can be expressed in 255 ways. a(9) = 28579081466859170 can be expressed in 511 ways. a(10) = 4069607103295265285 can be expressed in 1023 ways. CROSSREFS Cf. A300162, A300166, A300167. Sequence in context: A095027 A017781 A017728 * A004354 A016111 A217675 Adjacent sequences: A300165 A300166 A300167 * A300169 A300170 A300171 KEYWORD nonn,more,hard AUTHOR Hugo Pfoertner, Feb 27 2018 EXTENSIONS a(7) from Robert Price, Mar 11 2018 a(7) corrected, a(8)-a(9) added by Ray Chandler, Dec 23 2019 a(10) added by Ray Chandler, Dec 31 2019 STATUS approved

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Last modified September 10 20:50 EDT 2024. Contains 375794 sequences. (Running on oeis4.)