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A375269 Partial products of A115975.

%I A375269 #9 Aug 11 2024 10:35:11
%S A375269 1,2,6,24,120,840,6720,60480,665280,8648640,147026880,2793510720,
%T A375269 64250746560,1606268664000,43369253928000,1257708363912000,
%U A375269 38988959281272000,1247646697000704000,46162927789026048000,1892680039350067968000,81385241692052922624000,3825106359526487363328000
%N A375269 Partial products of A115975.
%C A375269 First differs from A334395 at n = 42.
%C A375269 Numbers with a record number of dual-Zeckendorf-infinitary divisors (A331109). Also, indices of records in A375272.
%C A375269 a(n) is the least number k such that A375272(k) = n-1 and A331109(k) = 2^(n-1).
%H A375269 Amiram Eldar, <a href="/A375269/b375269.txt">Table of n, a(n) for n = 1..358</a>
%F A375269 a(n) = Product_{k=1..n} A115975(k).
%e A375269 A115975 begins with 1, 2, 3, 4, 5, 7, ..., so, a(1) = 1, a(2) = 1 * 2 = 2, a(3) = 1 * 2 * 3 = 6, ..., a(6) = 1 * 2 * 3 * 4 * 5 * 7 = 840.
%t A375269 fib[lim_] := Module[{s = {}, f = 1, k = 2}, While[f <= lim, AppendTo[s, f]; k++; f = Fibonacci[k]]; s];
%t A375269 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[250]
%o A375269 (PARI) fib(lim) = {my(s = List(), f = 1, k = 2); while(f <= lim, listput(s, f); k++; f = fibonacci(k)); Vec(s);}
%o A375269 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 A375269 Cf. A037992 (analogous with "Fermi-Dirac primes", A050376), A115975, A331109, A334395, A375271, A375272.
%Y A375269 Subsequence of A025487.
%K A375269 nonn
%O A375269 1,2
%A A375269 _Amiram Eldar_, Aug 09 2024