A069459
a(n) = prime(n)^n - 1.
Original entry on oeis.org
1, 8, 124, 2400, 161050, 4826808, 410338672, 16983563040, 1801152661462, 420707233300200, 25408476896404830, 6582952005840035280, 925103102315013629320, 73885357344138503765448, 12063348350820368238715342, 3876269050118516845397872320, 1271991467017507741703714391418
Offset: 1
a(16) = A062457(n) - 1 = A000040(16)^16 - 1 = 53^16-1 =
= 3876269050118516845397872320 =
= 2^6*3^3*5*13*17*281*232073*31129845205681.
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[NthPrime(n)^n - 1: n in [1..25]]; // G. C. Greubel, Apr 22 2018
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Table[Prime[n]^n - 1, {n, 1, 25}] (* G. C. Greubel, Apr 22 2018 *)
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for(n=1, 25, print1(prime(n)^n - 1, ", ")) \\ G. C. Greubel, Apr 22 2018
A069463
Greatest prime factor of prime(n)^n+1.
Original entry on oeis.org
3, 5, 7, 1201, 13421, 28393, 22796593, 563377, 1117, 470925821, 1048563011, 3512477579761, 644522798011, 22021301, 24317675453761, 14189041365214758401, 21199857783625129028395239857, 13842121, 292354984050175817, 613624820402521
Offset: 1
A000040(10)^10+1 = 29^10+1 = 420707233300202 = 2*421*1061*470925821, therefore a(10) = 470925821.
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Table[FactorInteger[Prime[n]^n+1][[-1,1]],{n,20}] (* Harvey P. Dale, Aug 23 2019 *)
A191548
Smallest prime factor of prime(n)^n - 1 having the form k*n + 1.
Original entry on oeis.org
31, 5, 3221, 7, 25646167, 17, 19, 11, 23, 13, 11831, 5839, 31, 17, 137, 19, 751410597400064602523400427092397, 661, 127, 23, 47, 46644217, 101, 79, 2377, 29, 7193, 31, 1310825268269643509279336731098526398390609803239319801398048897, 97, 755569
Offset: 3
a(3) = 31 because prime(3)^3 - 1 = 5^3 - 1 = 124 = 2^2*31; the smallest prime divisor of the form k*n + 1 is 31 = 10*3 + 1 with k = 10.
Cf.
A069460 (greatest prime factor of prime(n)^n-1).
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Table[p = First /@ FactorInteger[Prime[n]^n - 1]; Select[p, Mod[#1, n] ==
1 &, 1][[1]], {n, 3, 30}]
Showing 1-3 of 3 results.
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