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

1, 2, 3, 4, 6, 8, 12, 16, 15, 18, 24, 32, 30, 36, 48, 64, 60, 72, 96, 128, 90, 120, 108, 144, 192, 256, 105, 180, 240, 216, 288, 384, 512, 210, 360, 480, 432, 576, 768, 1024, 420, 450, 540, 720, 648, 960, 864, 1152, 1536, 2048

Offset: 1

Author

Wolfdieter Lang, Mar 15 2011

Keywords

• nonn

Comments

For a list of the multiset repetition class defining partitions in Abramowitz-Stegun (A-St)order see the links under A176725 and A187447.

For the A-St ordering of all partitions see A036036.

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).

The analog sequence for all partitions in A-St order is A185974.

Examples

			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}.
		

Formula

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.