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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Marius A. Burtea, Table of n, a(n) for n = 1..150 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 Cf. A076942, A076944, A074792. Sequence in context: A365101 A329404 A370979 * A138228 A303722 A305225 Adjacent sequences: A076940 A076941 A076942 * A076944 A076945 A076946 KEYWORD nice,nonn AUTHOR Amarnath Murthy, Oct 19 2002 EXTENSIONS Edited, corrected and extended by Robert G. Wilson v, Oct 21 2002 STATUS approved

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Last modified August 6 00:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)