A382492 a(n) is the least number that has exactly n 3-smooth divisors.

1, 2, 4, 6, 16, 12, 64, 24, 36, 48, 1024, 72, 4096, 192, 144, 216, 65536, 288, 262144, 432, 576, 3072, 4194304, 864, 1296, 12288, 2304, 1728, 268435456, 2592, 1073741824, 3456, 9216, 196608, 5184, 6912, 68719476736, 786432, 36864, 10368, 1099511627776, 15552, 4398046511104

Offset: 1

Author

Amiram Eldar, Mar 29 2025

Keywords

• nonn
• easy

Comments

The record values occur at A046022.

All the terms are in A003586 and A025487.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3322

Crossrefs

Cf. A003586, A005179, A025487, A037143, A046022, A072078, A382493.

Programs

Mathematica

a[n_] := Min[Table[2^(d-1)*3^(n/d-1), {d, Divisors[n]}]]; Array[a, 60]

PARI

a(n) = vecmin(apply(d -> 2^(d-1)*3^(n/d-1), divisors(n)));

Formula

a(n) = Min_{d|n} (2^(d-1)*3^(n/d-1)).

a(n) = 2^A382493(n) * 3^(n/(A382493(n)+1)-1).

a(p) = 2^(p-1) for prime p.

a(n) = A005179(n) if n is in A037143.