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A231233
Triangle T(n,k) = greatest prime factor of n*k+1.
1
2, 3, 5, 2, 7, 5, 5, 3, 13, 17, 3, 11, 2, 7, 13, 7, 13, 19, 5, 31, 37, 2, 5, 11, 29, 3, 43, 5, 3, 17, 5, 11, 41, 7, 19, 13, 5, 19, 7, 37, 23, 11, 2, 73, 41, 11, 7, 31, 41, 17, 61, 71, 3, 13, 101, 3, 23, 17, 5, 7, 67, 13, 89, 5, 37, 61, 13, 5, 37, 7, 61, 73, 17, 97, 109, 11, 19, 29
OFFSET
1,1
LINKS
Étienne Fouvry, On the greatest prime factor of ab+1, arXiv:1311.1161 [math.NT], 2013.
FORMULA
T(n, k) = A006530(n*k+1).
EXAMPLE
Triangle begins:
2;
3, 5;
2, 7, 5;
5, 3, 13, 17;
3, 11, 2, 7, 13;
7, 13, 19, 5, 31, 37;
2, 5, 11, 29, 3, 43, 5;
MATHEMATICA
T[n_, k_] := FactorInteger[n k + 1][[-1, 1]];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 23 2018 *)
PROG
(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, f = factor(n*k+1); print1(f[#f~, 1], ", "); ); print(); ); }
(GAP) Flat(List([1..12], n->List([1..n], k->Maximum(FactorsInt(n*k+1))))); # Muniru A Asiru, Sep 23 2018
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Nov 06 2013
STATUS
approved