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.

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

Offset: 0

Author

Alford Arnold, May 02 2007

Keywords

• nonn

Comments

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

Examples

			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.