A096932 Smallest number having exactly s divisors, where s is the n-th semiprime (A001358).

6, 12, 36, 48, 192, 144, 576, 3072, 1296, 12288, 9216, 196608, 5184, 786432, 36864, 12582912, 46656, 589824, 82944, 2359296, 805306368, 3221225472, 331776, 37748736, 206158430208, 746496, 3298534883328, 5308416, 13194139533312, 2415919104, 2985984, 9663676416

Offset: 1

Author

Reinhard Zumkeller, Jul 15 2004

Keywords

• nonn

Comments

This is to smallest integer for which the number of divisors is the n-th prime (A061286) as semiprimes (A001358) are to primes (A000040). - Jonathan Vos Post, Feb 03 2011

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A001358, A005179, A061234, A061286, A061299, A084127.

Programs

Mathematica

s[n_] := Module[{f = FactorInteger[n], p, q}, If[Total[f[[;;,2]]] == 2, p=f[[1,1]]; q = n/p; 2^(q-1) * 3^(p-1) ,Nothing]]; Array[s, 100] (* Amiram Eldar, Apr 13 2024 *)

Formula

A000005(a(n)) = A001358(n) and A000005(m) <> A001358(n) for m < a(n).

a(n) = A005179(A001358(n)).

a(p*q) = 2^(q-1) * 3^(p-1) for primes p <= q.

a(A000040(i)*A000040(j)) = 2^(A084127(j)-1) * 3^(A084127(i)-1) for i <= j.