A050614 Products of distinct terms of A001566: a(n) = Product_{i=0..floor(log_2(n+1))} L(2^(i+1))^bit(n,i).

1, 3, 7, 21, 47, 141, 329, 987, 2207, 6621, 15449, 46347, 103729, 311187, 726103, 2178309, 4870847, 14612541, 34095929, 102287787, 228929809, 686789427, 1602508663, 4807525989, 10749959329, 32249877987, 75249715303

Offset: 0

Author

Antti Karttunen, Dec 02 1999

Keywords

• nonn

Comments

Each subset a(0..(2^k)-1) gives all the divisors of F(2^(k+1)) up to k=4 (F_32) and after that a subset of such divisors. E.g., the terms a(0)-a(7) are the divisors of F_16 = 987 (A018760).

Links

• Robert Price, Table of n, a(n) for n = 0..200
• A. Karttunen, On Pascal's Triangle Modulo 2 in Fibonacci Representation, Fibonacci Quarterly, 42 (2004), 38-46.

Crossrefs

Bisection of A075149 and A050613 (see there for the other Maple procedures), subset of A062877. Cf. also A050615.

Programs

Maple

[seq(A050614(n),n=0..30)]; A050614 := n -> product('luc(2^(i+1))^bit_i(n,i)','i'=0..floor_log_2(n+1));

Mathematica

Table[k = Floor[Log[2, n + 1]]; Product[j = 2^(i + 1); l = Fibonacci[j + 1] + Fibonacci[j - 1]; If[BitAnd[2^i, n] == 0, b = 0, b = 1]; l^b, {i, 0, k}], {n, 0, 200}] (* Robert Price, Feb 13 2017 *)

Formula

a(n) = Sum_{k=0..n} A127872(n,k)*Fibonacci(2*k+1), see A000045 and A001519. - Philippe Deléham, Aug 30 2007