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A375271 Partial products of A375270.

%I A375271 #8 Aug 11 2024 10:35:04
%S A375271 1,2,6,30,210,1680,18480,240240,4084080,77597520,1784742960,
%T A375271 48188059920,1397453737680,43321065868080,1602879437118960,
%U A375271 65718056921877360,2825876447640726480,132816193039114144560,7039258231073049661680,415316235633309930039120,25334290373631905732386320
%N A375271 Partial products of A375270.
%C A375271 Numbers with a record number of Zeckendorf-infinitary divisors (A318465). Also, indices of records in A318464.
%C A375271 a(n) is the least number k such that A318464(k) = n-1 and A318465(k) = 2^(n-1).
%H A375271 Amiram Eldar, <a href="/A375271/b375271.txt">Table of n, a(n) for n = 1..353</a>
%F A375271 a(n) = Product_{k=1..n} A375270(k).
%e A375271 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.
%t A375271 fib[lim_] := Module[{s = {}, f = 1, k = 2}, While[f <= lim, AppendTo[s, f]; k += 2; f = Fibonacci[k]]; s];
%t A375271 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]
%o A375271 (PARI) fib(lim) = {my(s = List(), f = 1, k = 2); while(f <= lim, listput(s, f); k += 2; f = fibonacci(k)); Vec(s);}
%o A375271 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, ", "))}
%Y A375271 Cf. A037992 (analogous with "Fermi-Dirac primes", A050376), A318464, A318465, A375270.
%Y A375271 Subsequence of A025487.
%K A375271 nonn
%O A375271 1,2
%A A375271 _Amiram Eldar_, Aug 09 2024