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

Author

Amiram Eldar, Aug 09 2024

Keywords

• nonn

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).

Examples

			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.
		

Links

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

Crossrefs

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

Subsequence of A025487.

Programs

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]

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, ", "))}

Formula

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