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%I #5 Apr 03 2013 22:51:29
%S 1,2,3,5,19,4,10,17,23,8,12,31,69,6,26,68,11,27,101,122,7,37,50,80,
%T 179,582,14,48,75,563,719,2820,4135,30,38,164,231,440,566,901,11093,
%U 112925,267167,212,9,65,374,20303,24,56,103,293,530,656,767,868,82,2157
%N Conjectured irregular triangle (with some rows blank) of numbers k such that prime(n) is the largest prime factor of k^3 + 1.
%C Primes 5, 11, 17, 23, 29, 47, 59,... do not appear as largest factors. However, they can be smaller factors. For instance, 4^3 + 1 = 5 * 13.
%e Irregular triangle:
%e 2: {1},
%e 3: {2},
%e 5: {},
%e 7: {3, 5, 19},
%e 11: {},
%e 13: {4, 10, 17, 23},
%e 17: {},
%e 19: {8, 12, 31, 69},
%e 23: {},
%e 29: {},
%e 31: {6, 26, 68},
%e 37: {11, 27, 101},
%e 41: {122},
%e 43: {7, 37, 50, 80, 179},
%e 47: {},
%e 53: {582},
%e 59: {},
%e 61: {14, 48, 75, 563, 719, 2820, 4135},
%e 67: {30, 38, 164, 231, 440, 566, 901, 11093, 112925, 267167},
%e 71: {212},
%e 73: {9, 65, 374, 20303},
%e 79: {24, 56, 103, 293, 530, 656, 767, 868},
%e 83: {82, 2157}.
%t t = Table[FactorInteger[n^3 + 1][[-1,1]], {n, 10^6}]; Table[Flatten[Position[t, Prime[n]]], {n, 25}]
%Y Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).
%Y Cf. A223701-A223707 (related sequences).
%K nonn,tabf
%O 1,2
%A _T. D. Noe_, Apr 03 2013
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