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A129305 Encodes multisets of least prime signatures in reverse-lex order: replace A036035 with A080688 then calculate all possible factorizations of the resulting values, recode each factor using A064553(n) and then multiply the terms. 2
1, 2, 4, 5, 6, 11, 8, 10, 17, 12, 15, 22, 31, 42, 69, 77, 86, 109, 16, 20, 25, 34, 47, 24, 30, 44, 55, 51, 62, 83, 36, 45, 66, 76, 95, 121, 93, 118, 149, 84, 105, 138, 154, 172, 215, 253, 201, 217, 218, 277, 546, 834, 861, 897, 994, 1001, 1118, 1529, 1633, 1763, 1041 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence A035310 counts the values in each sub-table and illustrates relationships with A000041, A000079, A000110 etc. Sequence A096443 counts the values associated with each least prime signature. (Cf. A025487 and A036035.)

LINKS

Table of n, a(n) for n=0..60.

EXAMPLE

The encoded values can be arranged in tabular form based on the number of factors and the associated numeric partitions as indicated below:

2..................................................

.....4.....5........................................

.....6.....11........................................

...............8.....10.....17.........................

...............12....15.....31.........................

.....................22..............................

...............42....69.....109.........................

.....................77..............................

.....................86..............................

.................................16.....20.....25.....34.....47

.................................24.....30.....55.....51.....83

........................................44............62.....

.................................36.....45.....95.....93.....149

........................................66.....121...118.....

........................................76...............

.................................84.....105.....215.....201.....277

........................................138.....253.....217.....

........................................154.............218.....

........................................172...............

................................546.....834.....1529.....1041.....1289

........................................861.....1633.....1138.....

........................................897.....1763.....1253.....

........................................994..............1417.....

........................................1001...............

........................................1118...............

CROSSREFS

Cf. A025487, A035310, A036035, A064553, A080688, A096443.

Sequence in context: A294812 A217354 A165701 * A278507 A113631 A202101

Adjacent sequences:  A129302 A129303 A129304 * A129306 A129307 A129308

KEYWORD

nonn

AUTHOR

Alford Arnold, May 02 2007

STATUS

approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)