A076944 -id:A076944 - cp's OEIS frontend

A074792 Least k > 1 such that k^n == 1 (mod n).

2, 3, 4, 3, 6, 5, 8, 3, 4, 9, 12, 5, 14, 13, 16, 3, 18, 5, 20, 3, 4, 21, 24, 5, 6, 25, 4, 13, 30, 11, 32, 3, 34, 33, 36, 5, 38, 37, 16, 3, 42, 5, 44, 21, 16, 45, 48, 5, 8, 9, 52, 5, 54, 5, 16, 13, 7, 57, 60, 7, 62, 61, 4, 3, 66, 23, 68, 13, 70, 29, 72, 5, 74, 73, 16, 37, 78, 17, 80, 3

Offset: 1

Benoit Cloitre, Sep 07 2002

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000

a(n) = {A076944(n)}^(1/n).

Cf. A076942, A076943, A076944.

Do[k = 2; While[ !IntegerQ[(k^n - 1)/n], k++ ]; Print[k], {n, 1, 80}] (* Robert G. Wilson v *)

a(n)=if(n<0,0,s=2; while((s^n-1)%n>0,s++); s)

a(n)=my(s=2); while(Mod(s,n)^n-1!=0, s++); return(s) \\ Rémy Sigrist, Apr 02 2017

If p is prime a(p)=p+1 and a(2p)=2p-1; if n is in A050384 a(n)=n+1; if n is in A067945 a(n)=3 etc. It seems that sum(k=1, n, a(k)) is asymptotic to c*n^2 with c=0.2...

A076943 Smallest k > 0 such that n*k + 1 is an n-th power.

Original entry on oeis.org

1, 4, 21, 20, 1555, 2604, 299593, 820, 29127, 348678440, 67546215517, 20345052, 61054982558011, 281241170407092, 76861433640456465, 2690420, 128583032925805678351, 211927625868, 275941052631578947368421, 174339220

Offset: 1

Amarnath Murthy, Oct 19 2002

			For n = 7, 1 + 7*a(7) = 1 + 7*299593 = 2097152 = 2^21 = 8^7.
For n = 10, 1 + 10*a(10) = 1 + 10*348678440 = 3486784401 = 3^20 = 9^10. - _Marius A. Burtea_, Jun 01 2019

Marius A. Burtea, Table of n, a(n) for n = 1..150

Cf. A076942, A076944, A074792.

sol:=[];
for u in [1..20] do
   for k in [2..100] do
      if IsIntegral((k^u-1)/u) then sol[u]:=(k^u-1)/u; break; end if;
   end for;
end for;
sol; // Marius A. Burtea, Jun 01 2019

Do[k = 2; While[ !IntegerQ[(k^n - 1)/n], k++ ]; Print[(k^n - 1)/n], {n, 1, 20}] (* Robert G. Wilson v, Oct 21 2002 *)

a(n) <= ((n+1)^n - 1) / n.
a(p^k) = ((p+1)^(p^k) - 1) / p^k. - Charlie Neder, May 23 2019
a(2*p) = ((2*p-1)^(2*p) - 1) / (2*p). - Charlie Neder, May 23 2019

Edited, corrected and extended by Robert G. Wilson v, Oct 21 2002

cp's OEIS Frontend

A074792 Least k > 1 such that k^n == 1 (mod n).

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