A096932 - OEIS

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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

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OFFSET

1,1

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

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.

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 *)

CROSSREFS

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

Sequence in context: A078402 A127845 A306899 * A376003 A212976 A352621

Adjacent sequences: A096929 A096930 A096931 * A096933 A096934 A096935

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 15 2004

STATUS

approved