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A223701 Irregular triangle of numbers k such that prime(n) is the largest prime factor of k^2 - 1. 7

%I #3 Apr 03 2013 22:49:06

%S 3,2,5,7,17,4,9,11,19,26,31,49,161,6,8,13,15,29,41,55,71,97,99,127,

%T 244,251,449,4801,8749,10,21,23,34,43,65,76,89,109,111,197,199,241,

%U 351,485,769,881,1079,6049,19601,12,14,25,27,51,53,64,79,129,131,155

%N Irregular triangle of numbers k such that prime(n) is the largest prime factor of k^2 - 1.

%C Note that the first number of each row forms the sequence 3, 2, 4, 6, 10, 12,..., which is A039915. The rows, except the first, are in A181447-A181470.

%e Irregular triangle:

%e {3},

%e {2, 5, 7, 17},

%e {4, 9, 11, 19, 26, 31, 49, 161},

%e {6, 8, 13, 15, 29, 41, 55, 71, 97, 99, 127, 244, 251, 449, 4801, 8749}

%t t = Table[FactorInteger[n^2 - 1][[-1,1]], {n, 2, 10^5}]; Table[1 + Flatten[Position[t, Prime[n]]], {n, 6}]

%Y Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).

%Y Cf. A181447-A181470.

%Y Cf. A223702-A223707 (related sequences).

%K nonn,tabf

%O 1,1

%A _T. D. Noe_, Apr 03 2013

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