A279623 -id:A279623 - cp's OEIS frontend

A280104 a(n) = smallest prime factor of n-th Lucas number A000032(n), or 1 if there are none.

2, 1, 3, 2, 7, 11, 2, 29, 47, 2, 3, 199, 2, 521, 3, 2, 2207, 3571, 2, 9349, 7, 2, 3, 139, 2, 11, 3, 2, 7, 59, 2, 3010349, 1087, 2, 3, 11, 2, 54018521, 3, 2, 47, 370248451, 2, 6709, 7, 2, 3, 6643838879, 2, 29, 3, 2, 7, 119218851371, 2, 11, 47, 2, 3, 709, 2

Offset: 0

Vincenzo Librandi, Dec 26 2016

nonn

From Robert Israel, Jan 05 2017: (Start)
If m and n are odd, m > 1 and m | n, then a(n) <= a(m).
a(n) = 2 if and only if 3 | n.
a(n) = 3 if and only if n is in A091999.
a(n) is never 5.
a(n) = 7 if and only if n is in A259755.
a(n) = A000032(n) if and only if n is in A001606.
(End)

Robert Israel, Table of n, a(n) for n = 0..1000
Fibonacci and Lucas Factorizations

Cf. A000032, A001606, A020639, A079451 (same for largest prime factor), A091999, A139044, A144293, A259755, A279623.

Column k=2 of A238899 (for n>=2).

[2,1] cat [Minimum(PrimeDivisors(Lucas(n))): n in [2..60]];

lucas:= n -> combinat:-fibonacci(n+1)+combinat:-fibonacci(n-1):
spf:= proc(n) local F;
  F:= remove(hastype,ifactors(n,easy)[2],symbol);
  if F <> [] then return min(seq(f[1],f=F)) fi;
min(numtheory:-factorsec(n))
end proc:
spf(1):= 1:
map(spf @ lucas, [$0..200]); # Robert Israel, Jan 05 2017

f[n_]:=(FactorInteger@LucasL@n)[[1, 1]]; Array[f, 60, 0]

a000032(n) = fibonacci(n+1)+fibonacci(n-1)
a(n) = if(a000032(n-1)==1, 1, factor(a000032(n-1))[1, 1]) \\ Felix Fröhlich, Dec 26 2016

a(n) = A020639(A000032(n)). - Felix Fröhlich, Dec 26 2016

Offset changed from Bruno Berselli, Dec 27 2016

A377801 Irregular triangle read by rows: row n lists divisors of n-th Bell number.

Original entry on oeis.org

1, 1, 1, 2, 1, 5, 1, 3, 5, 15, 1, 2, 4, 13, 26, 52, 1, 7, 29, 203, 1, 877, 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 30, 36, 45, 46, 60, 69, 90, 92, 115, 138, 180, 207, 230, 276, 345, 414, 460, 690, 828, 1035, 1380, 2070, 4140, 1, 3, 7, 19, 21, 53, 57, 133, 159, 371, 399, 1007, 1113, 3021, 7049, 21147

Offset: 0

Vincenzo Librandi, Nov 07 2024

			Triangle begins:
  1,
  1,
  1,   2,
  1,   5,
  1,   3,  5,  15,
  1,   2,  4,  13, 26, 52,
  1,   7, 29, 203,
  1, 877,
  ...

Amiram Eldar, Table of n, a(n) for n = 0..7035 (rows 0..103 flattened)

Cf. A000110, A027750, A279623.
Row sums give A262349.
Row lengths give A278973.

/* As triangle */ [Divisors(Bell(n)): n in [0..30]];

Flatten[Table[Divisors[BellB[n]], {n, 0, 20}]]

T(n,k) = A027750(A000110(n),k).

T(n,2) = A279623(n) for n>=2.

cp's OEIS Frontend

A280104 a(n) = smallest prime factor of n-th Lucas number A000032(n), or 1 if there are none.

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