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A076943
Smallest k > 0 such that n*k + 1 is an n-th power.
7
1, 4, 21, 20, 1555, 2604, 299593, 820, 29127, 348678440, 67546215517, 20345052, 61054982558011, 281241170407092, 76861433640456465, 2690420, 128583032925805678351, 211927625868, 275941052631578947368421, 174339220
OFFSET
1,2
LINKS
FORMULA
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
EXAMPLE
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
MATHEMATICA
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 *)
PROG
(Magma) 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
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Amarnath Murthy, Oct 19 2002
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Oct 21 2002
STATUS
approved