cp's OEIS Frontend

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

%I A273772 #43 Sep 24 2024 11:26:58
%S A273772 381713,58651,12301,2861,1656278791,547,5179643,214,2719331,26627,
%T A273772 73651287679,90205,5069,5533707,13117,58385,791716066017,5589,
%U A273772 21214381292,3802401,509437122973,167,1261552,6001,1144853,3111,6952504,143573
%N A273772 Least k > 1 such that n*(k*n-1) - 1 divides n^(k*n-1) - 1, or 0 if no such k exists.
%C A273772 Is gcd(n, a(n)) = 1? - _David A. Corneth_, Jun 02 2016
%C A273772 No: gcd(15, a(15)) = 3. - _Charles R Greathouse IV_, Jun 04 2016
%C A273772 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
%C A273772 1.1*10^16 < a(30) <= 123676617214883421968465. - _Max Alekseyev_, Sep 24 2024
%o A273772 (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
%Y A273772 Cf. A233415, A273727.
%K A273772 nonn,more
%O A273772 2,1
%A A273772 _Juri-Stepan Gerasimov_, May 29 2016
%E A273772 a(3) corrected by _Charles R Greathouse IV_, Jun 02 2016
%E A273772 a(6)-a(17) from _Charles R Greathouse IV_, Jun 04 2016
%E A273772 a(18)-a(29) from _Lucas A. Brown_, Feb 28 2024