A280104 -id:A280104 - cp's OEIS frontend

A079451 Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.

2, 1, 3, 2, 7, 11, 3, 29, 47, 19, 41, 199, 23, 521, 281, 31, 2207, 3571, 107, 9349, 2161, 211, 307, 461, 1103, 151, 90481, 5779, 14503, 19489, 2521, 3010349, 4481, 9901, 63443, 911, 103681, 54018521, 29134601, 859, 3041, 370248451, 1427, 144481, 967, 541, 275449

Offset: 0

Lekraj Beedassy, Jan 13 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 0..1000 (using Blair Kelly's data)
J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.
Blair Kelly, Factorizations of first 1000 Lucas numbers.

Cf. A000032 (Lucas numbers), A006530 (greatest prime factor).
Cf. A001606 (indices of prime Lucas numbers <=> where a(n) = A000032(n)), subsequence of A076697 (indices of record values in this sequence).
Cf. A280104 (same for smallest prime factor).

[2,1] cat [Maximum(PrimeDivisors(Lucas(n))): n in [2..60]]; // Vincenzo Librandi, Dec 26 2016

A079451 := proc(n)
        A006530(A000032(n)) ;
end proc:
seq(A079451(n),n=0..30) ; # R. J. Mathar, Oct 26 2013
# second Maple program:
a:= n-> max(ifactors((<<1|1>, <1|0>>^n. <<2, -1>>)[1, 1])[2][..., 1][], 1):
seq(a(n), n=0..46);  # Alois P. Heinz, Aug 04 2025

Join[{2,1},f[n_]:=(FactorInteger@LucasL@n)[[-1,1]];Array[f,60,2]] (* Vincenzo Librandi, Dec 26 2016 *)

a(n) = my(f = factor(fibonacci(n+1)+fibonacci(n-1))); if (om = #f~, f[om, 1], 1); \\ Michel Marcus, Oct 26 2013

A079451(n) = A006530(A000032(n)) \\ M. F. Hasler, Apr 10 2025

def A079451(n): return A006530(A000032(n)) # M. F. Hasler, Apr 10 2025

a(n) = A006530(A000032(n)). - Felix Fröhlich, Dec 26 2016

More terms from Michel Marcus, Oct 26 2013

Modified b-file and scripts so that a(1)=1. - David Radcliffe, Aug 03 2025

A238899 Irregular triangle read by rows: row n lists divisors of n-th Lucas number A000032(n).

Original entry on oeis.org

1, 2, 1, 1, 3, 1, 2, 4, 1, 7, 1, 11, 1, 2, 3, 6, 9, 18, 1, 29, 1, 47, 1, 2, 4, 19, 38, 76, 1, 3, 41, 123, 1, 199, 1, 2, 7, 14, 23, 46, 161, 322, 1, 521, 1, 3, 281, 843, 1, 2, 4, 11, 22, 31, 44, 62, 124, 341, 682, 1364, 1, 2207, 1, 3571, 1, 2, 3, 6, 9, 18, 27, 54

Offset: 0

T. D. Noe, Mar 14 2014

Note that, in general, the Lucas numbers have fewer divisors than Fibonacci numbers. Why?

			Triangle begins:
  1,   2;
  1;
  1,   3;
  1,   2,  4;
  1,   7;
  1,  11;
  1,   2,  3,   6,  9, 18;
  1,  29;
  1,  47;
  1,   2,  4,  19, 38, 76;
  1,   3, 41, 123;
  1, 199;
  1,   2,  7,  14, 23, 46, 161, 322;
  ...

T. D. Noe, Rows 0 to 100 of irregular triangle, flattened

Cf. A000032 (Lucas numbers), A027750.
Cf. A133021 (similar triangle for Fibonacci numbers).
Column 2 gives A280104 (for n>=2).

[Divisors(Lucas(n)): n in [0..30]]; // Vincenzo Librandi, Nov 15 2024

Flatten[Table[Divisors[LucasL[n]], {n, 0, 20}]] (* Typo corrected by Harvey P. Dale, Jun 29 2021 *)

A364820 a(n) is the smallest prime factor of the n-th Pell number A000129(n).

Original entry on oeis.org

2, 5, 2, 29, 2, 13, 2, 5, 2, 5741, 2, 33461, 2, 5, 2, 137, 2, 37, 2, 5, 2, 229, 2, 29, 2, 5, 2, 44560482149, 2, 61, 2, 5, 2, 13, 2, 593, 2, 5, 2, 1746860020068409, 2, 11437, 2, 5, 2, 3761, 2, 13, 2, 5, 2, 68480406462161287469, 2, 29, 2, 5, 2

Offset: 2

Sean A. Irvine, Oct 21 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 2..630

Cf. A246556 (smallest primitive factor), A264137, A280104, A060383, A020639.

FactorInteger[#][[1, 1]] & /@ LinearRecurrence[{2, 1}, {2, 5}, 57] (* Amiram Eldar, Oct 21 2023 *)

a(n) = A020639(A000129(n)).

cp's OEIS Frontend

A079451 Largest prime dividing the n-th Lucas number (A000032); 1 when no such prime exists.

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A238899 Irregular triangle read by rows: row n lists divisors of n-th Lucas number A000032(n).

Views

Author

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Examples

Links

Crossrefs

Programs

Magma

Mathematica

A364820 a(n) is the smallest prime factor of the n-th Pell number A000129(n).

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula