OFFSET
1,2
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.
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.
EXAMPLE
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}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Mar 15 2011
STATUS
approved