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A187448 One half of the smallest number with prime signature of the multiset defining partition, taken in Abramowitz-Stegun order. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..50.

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

Sequence in context: A300787 A171966 A034893 * A321266 A018662 A240557

Adjacent sequences:  A187445 A187446 A187447 * A187449 A187450 A187451

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Mar 15 2011

STATUS

approved

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Last modified May 25 02:12 EDT 2022. Contains 354047 sequences. (Running on oeis4.)