A346491 Number of factorizations of the n-th Fibonacci number.

1, 1, 1, 1, 1, 3, 1, 2, 2, 2, 1, 29, 1, 2, 5, 5, 1, 21, 2, 15, 5, 2, 1, 719, 4, 2, 15, 15, 1, 296, 2, 15, 5, 2, 5, 4323, 5, 5, 5, 203, 2, 296, 1, 52, 52, 5, 1, 32653, 5, 135, 5, 15, 2, 1315, 15, 566, 52, 5, 2, 270920, 2, 5, 52, 203, 5, 296, 5, 52, 52, 877, 2

Offset

1,6

Links

Alois P. Heinz, Table of n, a(n) for n = 1..119

Formula

a(n) = A001055(A000045).

a(n) = A001055(A046523(A000045(n))).

a(n) = A001055(A278245(n)).

a(n) = 1 <=> n in { A001605 } union {1,2}.

a(n) = 2 <=> n in { A072381 }.

Maple

b:= proc(n, k) option remember; `if`(n>k, 0, 1)+`if`(isprime(n), 0,
      add(`if`(d>k, 0, b(n/d, d)), d=numtheory[divisors](n) minus {1, n}))
    end:
a:= proc(n) option remember; b((l-> mul(ithprime(i)^l[i], i=1..nops(l)))(
      sort(map(i-> i[2], ifactors(combinat[fibonacci](n))[2]), `>`))$2)
    end:
seq(a(n), n=1..80);

Mathematica

T[_, 1] = T[1, _] = 1;
T[n_, m_] := T[n, m] = DivisorSum[n, If[1 < # <= m, T[n/#, #], 0]&];
f[n_] := T[n, n];
a[n_] := f[Fibonacci[n]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 119}] (* Jean-François Alcover, Sep 08 2022 *)

Crossrefs

Cf. A000045, A001055, A001605, A046523, A072381, A278245.

Sequence in context: A225849 A038575 A347430 * A304302 A305516 A305182

Adjacent sequences: A346488 A346489 A346490 * A346492 A346493 A346494

Keyword

nonn

Author

Alois P. Heinz, Jul 19 2021

Status

approved