A075377 Triangle read by rows in which n-th row gives all values of n!/{(p!)^a*(q!)^b*(r!)^c*...} (in increasing order) for all factorizations n = p^a*q^b*r^c*....

1, 1, 1, 1, 6, 1, 1, 60, 1, 1, 840, 5040, 1, 10080, 1, 15120, 1, 1, 332640, 3326400, 19958400, 1, 1, 8648640, 1, 1816214400, 1, 259459200, 36324288000, 217945728000, 1307674368000, 1, 1, 8821612800, 1482030950400, 88921857024000, 1, 1

Offset

1,5

Comments

This is a modification of A036038.

A001055 gives the row lengths. - David Wasserman, Jan 17 2005

References

Amarnath Murthy, Generalization of partition function,Introducing Smarandache Factor Partition, Smarandache Notions Journal, Vol. 11, 2000.

Links

Table of n, a(n) for n=1..38.

Example

The row for n = 12 is: 1, 332640, 3326400, 19958400, since 12 = 12, 6*2, 4*3, 3*2*2.
Triangle begins:
1
1
1
1 6
1
1 60
1
1 840 5040
1 10080
1 15120
1
1 332640 3326400 19958400
1
1 8648640
1 1816214400
1 259459200 36324288000 217945728000 1307674368000
1
1 8821612800 1482030950400 88921857024000
1
1 335221286400 844757641728000 5068545850368000

Crossrefs

Cf. A036038, A001055, A036038.

Sequence in context: A015117 A287020 A172375 * A046792 A209330 A357297

Adjacent sequences: A075374 A075375 A075376 * A075378 A075379 A075380

Keyword

tabf,nonn

Author

Amarnath Murthy, Sep 21 2002

Extensions

More terms from David Wasserman, Jan 17 2005

Status

approved