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

1,2

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

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A355303 A099315 A005179 * A037019 A369099 A341668

Adjacent sequences: A382489 A382490 A382491 * A382493 A382494 A382495

Keyword

nonn,easy

Author

Amiram Eldar, Mar 29 2025

Status

approved