A375271 Partial products of A375270.

1, 2, 6, 30, 210, 1680, 18480, 240240, 4084080, 77597520, 1784742960, 48188059920, 1397453737680, 43321065868080, 1602879437118960, 65718056921877360, 2825876447640726480, 132816193039114144560, 7039258231073049661680, 415316235633309930039120, 25334290373631905732386320

Offset

1,2

Comments

Numbers with a record number of Zeckendorf-infinitary divisors (A318465). Also, indices of records in A318464.

a(n) is the least number k such that A318464(k) = n-1 and A318465(k) = 2^(n-1).

Links

Amiram Eldar, Table of n, a(n) for n = 1..353

Formula

a(n) = Product_{k=1..n} A375270(k).

Example

A375270 begins with 1, 2, 3, 5, ..., so, a(1) = 1, a(2) = 1 * 2 = 2, a(3) = 1 * 2 * 3 = 6, a(4) = 1 * 2 * 3 * 5 = 30.

Mathematica

fib[lim_] := Module[{s = {}, f = 1, k = 2}, While[f <= lim, AppendTo[s, f]; k += 2; f = Fibonacci[k]]; s];
seq[max_] := Module[{s = {}, p = 2, e = 1, f = {}}, While[e > 0, e = Floor[Log[p, max]]; If[f == {}, f = fib[e], f = Select[f, # <= e &]]; s = Join[s, p^f]; p = NextPrime[p]]; FoldList[Times, 1, Sort[s]]]; seq[100]

Prog

(PARI) fib(lim) = {my(s = List(), f = 1, k = 2); while(f <= lim, listput(s, f); k += 2; f = fibonacci(k)); Vec(s); }
lista(pmax) = {my(s = [1], p = 2, e = 1, f = [], r = 1); while(e > 0, e = logint(pmax, p); if(#f == 0, f = fib(e), f = select(x -> x <= e, f)); s = concat(s, apply(x -> p^x, f)); p = nextprime(p+1)); s = vecsort(s); for(i = 1, #s, r *= s[i]; print1(r, ", "))}

Crossrefs

Cf. A037992 (analogous with "Fermi-Dirac primes", A050376), A318464, A318465, A375270.

Subsequence of A025487.

Sequence in context: A372741 A118747 A377707 * A129779 A068215 A305400

Adjacent sequences: A375268 A375269 A375270 * A375272 A375273 A375274

Keyword

nonn

Author

Amiram Eldar, Aug 09 2024

Status

approved