A274567 Least number k such that k^2-1 is the sum of two nonzero squares in exactly n ways.

3, 81, 51, 291, 1251, 339, 62499, 1971, 5201, 5001, 175781251, 7299, 17578125001, 31251, 66249, 12819

Offset

1,1

Comments

a(17) <= 610351562499. - David A. Corneth, Jul 23 2020

Links

Table of n, a(n) for n=1..16.

Example

a(2) = 81 because 81^2 - 1 = 28^2 + 76^2 = 44^2 + 68^2.

Prog

(PARI) A025426(n) = my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f~, if(f[i, 1]%4>1, if(f[i, 2]%2, return(0)), t*=f[i, 2]+1)); if(t%2, t-(-1)^v, t)/2;
a(n) = my(k=2); while(A025426(k^2-1)!=n, k++); k; \\ Michel Marcus, Sep 22 2025

Crossrefs

Cf. A000404, A005563, A016032, A025426, A050795, A050797, A054994.

Sequence in context: A233124 A251694 A355626 * A137994 A074386 A116009

Adjacent sequences: A274564 A274565 A274566 * A274568 A274569 A274570

Keyword

nonn,more

Author

Altug Alkan, Jun 28 2016

Extensions

a(10) from Chai Wah Wu, Jul 22 2020

a(13) from David A. Corneth confirmed and a(14)-a(16) added by Max Alekseyev, Sep 21 2025

Status

approved