A273772 Least k > 1 such that n*(k*n-1) - 1 divides n^(k*n-1) - 1, or 0 if no such k exists.

381713, 58651, 12301, 2861, 1656278791, 547, 5179643, 214, 2719331, 26627, 73651287679, 90205, 5069, 5533707, 13117, 58385, 791716066017, 5589, 21214381292, 3802401, 509437122973, 167, 1261552, 6001, 1144853, 3111, 6952504, 143573

Offset: 2

Author

Juri-Stepan Gerasimov, May 29 2016

Keywords

• nonn
• more

Comments

Is gcd(n, a(n)) = 1? - David A. Corneth, Jun 02 2016

No: gcd(15, a(15)) = 3. - Charles R Greathouse IV, Jun 04 2016

If a(30) is not 0, then it exceeds 5 * 10^12. Terms a(31) through a(34) are 4219, 124522631, 305201, and 6475739899. - Lucas A. Brown, Feb 28 2024

1.1*10^16 < a(30) <= 123676617214883421968465. - Max Alekseyev, Sep 24 2024

Crossrefs

Cf. A233415, A273727.

Programs

PARI

a(n)=my(k=2,n2=n^2); while(Mod(n,k*n2-n-1)^(k*n-1)!=1, k++); k \\ Charles R Greathouse IV, Jun 02 2016

Extensions

a(3) corrected by Charles R Greathouse IV, Jun 02 2016

a(6)-a(17) from Charles R Greathouse IV, Jun 04 2016

a(18)-a(29) from Lucas A. Brown, Feb 28 2024