cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A061148 #11 Jun 21 2019 12:16:00
%S A061148 12,48,192,144,576,3072,12288,9216,196608,5184,786432,36864,12582912,
%T A061148 589824,82944,2359296,805306368,3221225472,331776,37748736,
%U A061148 206158430208,746496,3298534883328,5308416,13194139533312,2415919104
%N A061148 Smallest positive integer for which the number of divisors is a product of 2 distinct primes: Min{x; d[x]=pq}.
%C A061148 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].
%C A061148 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.
%H A061148 Amiram Eldar, <a href="/A061148/b061148.txt">Table of n, a(n) for n = 1..563</a>
%F A061148 a(n) = A005179(A006881(n)).
%e A061148 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.
%Y A061148 Cf. A000005, A006881, A005117, A005179.
%K A061148 nonn
%O A061148 1,1
%A A061148 _Labos Elemer_, May 30 2001