A061148 Smallest positive integer for which the number of divisors is a product of 2 distinct primes: Min{x; d[x]=pq}.

12, 48, 192, 144, 576, 3072, 12288, 9216, 196608, 5184, 786432, 36864, 12582912, 589824, 82944, 2359296, 805306368, 3221225472, 331776, 37748736, 206158430208, 746496, 3298534883328, 5308416, 13194139533312, 2415919104

Offset

1,1

Comments

Least solutions of d(x)=A000005(x)=pq equation, where 1<p<q, primes: x=(2^q)*(3^p) where the exponent of smaller base[=2] is the larger prime factor[=q].

Since 2^(pq-1)>2^(q-1)*3^(p-1) -> [(2^q)/3]^(p-1) holds for q>1, p>1, therefore these solutions are in fact minimal.

Links

Amiram Eldar, Table of n, a(n) for n = 1..563

Formula

a(n) = A005179(A006881(n)).

Example

If d(x)=253=11*23, then 1<p=11<q=23,q-1=22,p-1=10, 2^22=4194304, 3^10=59049 so the smallest number x, which has 253 divisors is 4194304*59049=247669456896.

Crossrefs

Cf. A000005, A006881, A005117, A005179.

Sequence in context: A117027 A161171 A007200 * A339760 A221908 A242026

Adjacent sequences: A061145 A061146 A061147 * A061149 A061150 A061151

Keyword

nonn

Author

Labos Elemer, May 30 2001

Status

approved