A174524 The total number of factors in unordered factorizations of A025487(n) (Least Prime signatures).

0, 1, 3, 3, 6, 8, 12, 17, 10, 20, 22, 34, 27, 35, 46, 61, 60, 54, 94, 75, 107, 37, 101, 123, 86, 170, 170, 176, 104, 207, 230, 128, 304, 356, 284, 242, 386, 217, 413, 192, 397, 506, 303, 434, 680, 442, 512, 698, 502, 703, 275, 847, 832, 151, 725, 818, 1244, 676, 993, 1190, 1079, 1162, 399, 1654, 1311, 446, 1572, 1501, 1207, 2158, 1007, 917, 1840, 1831, 1980, 2104, 1785, 1859, 1579, 556

Offset

1,3

Comments

A025487(n) has a certain number of unordered factorizations with between 1 and A001222(A025487(n)) factors.

a(n) counts these factors that are >1. A025487(5) counts 8, 2*4, 2*2*2 with 1+2+3=6=a(5) factors, for example.

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = A066637(A025487(n)). [ R. J. Mathar, Oct 03 2010]

Example

The table of factorizations in A162247 begins:
1
2
3
4 2 2
5
6 2 3
7
8 2 4 2 2 2
9 3 3
10 2 5
11
12 2 6 3 4 2 2 3
A025487(n) begins 1 2 4 6 8 12 ...
a(n) counts the elements larger than 1 in the A025487(n)-th row of A162247: 0 1 3 3 6 8 ...

Crossrefs

Cf. A025487, A162247

Sequence in context: A241831 A239946 A130780 * A143592 A280197 A333526

Adjacent sequences: A174521 A174522 A174523 * A174525 A174526 A174527

Keyword

easy,nonn

Author

Alford Arnold, Mar 21 2010

Extensions

a(1) replaced by 0. Sequence extended - R. J. Mathar, Oct 03 2010

Status

approved