A382293 a(n) is the least number k such that A382290(k) = n.

1, 8, 128, 3456, 279936, 34992000, 8957952000, 3072577536000, 1920360960000000, 2556000437760000000, 5615532961758720000000, 13482894641182686720000000, 66241461372130539855360000000, 434610228062548471991016960000000, 2980991554281019969386385328640000000

Offset: 0

Author

Amiram Eldar, Mar 21 2025

Keywords

• nonn

Comments

Also, a(n) is the least number k such that A382291(k) = 2^n.

Cumulative products of the sorted sequence that contains 1 and prime powers of the form p^3 and p^(2^k) with k >= 2.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..150

Crossrefs

Subsequence of A025487.

Cf. A037992, A050376, A382290, A382291.

Programs

Mathematica

seq[max_] := Module[{t = {}, k = 3, lim}, While[lim = max^(1/k); lim > 2, t = Join[t, Prime[Range[PrimePi[lim]]]^k]; If[k == 3, k = 4, k *= 2]]; t = Sort[t]; FoldList[Times, 1, t]]; seq[10^4] (* after T. D. Noe at A050376 *)

PARI

list(mx) = {my(t = [1], k =3, lim); while(lim = mx^(1/k); lim > 2, t = concat(t, apply(x -> x^k, primes(primepi(lim)))); if(k == 3, k = 4, k *= 2)); t = vecsort(t); vector(#t, n, prod(i = 1, n, t[i]));}