A274347 -id:A274347 - cp's OEIS frontend

A274349 Products of two distinct Lucas numbers (2,3,4,7,11,18,...).

6, 8, 12, 14, 21, 22, 28, 33, 36, 44, 54, 58, 72, 77, 87, 94, 116, 126, 141, 152, 188, 198, 203, 228, 246, 304, 319, 329, 369, 398, 492, 517, 522, 532, 597, 644, 796, 836, 846, 861, 966, 1042, 1288, 1353, 1363, 1368, 1393, 1563, 1686, 2084, 2189, 2204, 2214

Offset: 1

Clark Kimberling, Jun 18 2016

			6 = 2*3, 44 = 4*11.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000032, A274348, A274347, A271354.

N:= 10000: # for terms <= N
L:= gfun:-rectoproc({f(n)=f(n-1)+f(n-2),f(0)=2,f(1)=1},f(n),remember):
S:= {}:
for i from 2 do
  u:= L(i);
  if u > N then break fi;
  for j from 0 to i-1 do
    if j = 1 then next fi;
    v:= u*L(j);
    if v > N then break fi;
    S:= S union {v};
od od:
sort(convert(S,list)); # Robert Israel, Jan 01 2021

z = 100; f[n_] := LucasL[n]; f[1] = 2 ;
Take[Sort[Flatten[Table[f[u] f[v], {u, 1, z}, {v, 1, u - 1}]]], z]
Take[Times@@@Subsets[Join[{2},LucasL[Range[2,20]]],{2}]//Union,60] (* Harvey P. Dale, Aug 13 2019 *)

A274374 Products of 2 distinct Fibonacci numbers and products of two distinct Lucas numbers (without 2), arranged in increasing order.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 18, 21, 24, 26, 28, 29, 33, 34, 39, 40, 42, 44, 47, 54, 55, 63, 65, 68, 72, 76, 77, 87, 89, 102, 104, 105, 110, 116, 123, 126, 141, 144, 165, 168, 170, 178, 188, 198, 199, 203, 228, 233, 267, 272, 273, 275, 288

Offset: 1

Clark Kimberling, Jun 19 2016

Are 3 and 21 the only numbers that are a product of two distinct Fibonacci numbers and also a product of two distinct Lucas numbers?

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A049862, A274347, A274375.

z = 400; f[n_] := Fibonacci[n];
s = Join[{0}, Take[Sort[Flatten[Table[f[m] f[n], {n, 2, z}, {m, 2, n - 1}]]], z]]
g[n_] := LucasL[n]; t = Take[Sort[Flatten[Table[g[u] g[v], {u, 1, z}, {v, 1, u - 1}]]], z]
Union[s, t]

A274353 Number of factors L(i) > 1 of A274280(n), where L = A000032 (Lucas numbers, 1,3,4,...)

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 3, 2, 2, 1, 2, 3, 2, 2, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 2, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 1, 2, 3, 2

Offset: 1

Clark Kimberling, Jun 18 2016

			The products of distinct Lucas numbers, arranged in increasing order, comprise A274280.  The list begins with 1, 3, 4, 7, 11, 12 = 3*4, so that a(6) = 2.

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A000032, A274280, A274347, A274348, A160009, A272947, A274354.

r[1] := 1; r[2] := 3; r[n_] := r[n] = r[n - 1] + r[n - 2];
s = {1}; z = 40; f = Map[r, Range[z]]; Take[f, 10]
Do[s = Union[s, Select[s*f[[i]], # <= f[[z]] &]], {i, z}];
infQ[n_] := MemberQ[f, n];
a = Table[#[[Flatten[Position[Map[Apply[Times, #] &, #], s[[n]]]][[1]]]] &[
Rest[Subsets[Map[#[[1]] &, Select[Map[{#, infQ[#]} &,
Divisors[s[[n]]]], #[[2]] && #[[1]] > 1 &]]]]], {n, 2, 200}];
ans = Join[{{1}}, a]; Take[ans, 8]
w = Map[Length, ans] (* A274353 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 2 &]] (* A274347 *)
Map[Apply[Times, #] &, Select[ans, Length[#] == 3 &]] (* A274348 *)
(* Peter J. C. Moses, Jun 17 2016 *)

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A274349 Products of two distinct Lucas numbers (2,3,4,7,11,18,...).

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A274374 Products of 2 distinct Fibonacci numbers and products of two distinct Lucas numbers (without 2), arranged in increasing order.

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A274353 Number of factors L(i) > 1 of A274280(n), where L = A000032 (Lucas numbers, 1,3,4,...)

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