cp's OEIS Frontend

A187448 One half of the smallest number with prime signature of the multiset defining partition, taken in Abramowitz-Stegun order.

%I A187448 #8 Mar 14 2015 00:59:29
%S A187448 1,2,3,4,6,8,12,16,15,18,24,32,30,36,48,64,60,72,96,128,90,120,108,
%T A187448 144,192,256,105,180,240,216,288,384,512,210,360,480,432,576,768,1024,
%U A187448 420,450,540,720,648,960,864,1152,1536,2048
%N A187448 One half of the smallest number with prime signature of the multiset defining partition, taken in Abramowitz-Stegun order.
%C A187448 For a list of the multiset repetition class defining partitions in Abramowitz-Stegun (A-St)order see the links under A176725 and A187447.
%C A187448 For the A-St ordering of all partitions see A036036.
%C A187448 The actual sequence is 2*a(n): 2, 4, 6, 8, 12, 16, 24, 32, 30, 36, 48, 64, 60, 72, 96, 128, 120, 144, 192, 256,...  This is similar to A025487 without the leading 1 (products of primorial numbers A002110, ordered increasingly, which is not the case here).
%C A187448 The analog sequence for all partitions in A-St order is  A185974.
%F A187448 a(n)=((p(1)^e[1])*(p(2)^e^[2])*...*(p(M)^e[M]))/2 with the prime numbers p(j):=A000040(j), and the n-th multiset defining partition with positive integer exponents e[1]>=e[2]>=...>=e[M]>=1; M=M(n)=A176725(n), read as sequence. These partitions are taken in A-St order. See the links to A176725 and A187447 for this partition list.
%e A187448 2*a(11)=2*24=48 =2^4*3^1, the smallest number with prime signature e[1]=4, e[2]=1, read as multiset defining partition 1^4,2^1, which is the 11th one in Abramowitz-Stegun order. The corresponding 5-multiset is {1,1,1,1,2}.
%K A187448 nonn
%O A187448 1,2
%A A187448 _Wolfdieter Lang_, Mar 15 2011