

A095705


Triangular array read by rows: a(n, k) = sum of number of ordered factorizations of all prime signatures with n total prime factors and k distinct prime factors.


5



1, 2, 3, 4, 8, 13, 8, 46, 44, 75, 16, 124, 308, 308, 541, 32, 572, 1790, 2536, 2612, 4683, 64, 1568, 8352, 17028, 24704, 25988, 47293, 128, 6728, 40628, 137498, 187928, 277456, 296564, 545835, 256, 18768, 228308, 719056, 1699184, 2356560, 3526448
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OFFSET

1,2


COMMENTS

A093936 is an analogous array for unordered factorizations.
First column is A000079. First two diagonals are A000670 and A005649.


LINKS

Table of n, a(n) for n=1..43.


EXAMPLE

There are two prime signatures with 5 total primes and 3 distinct primes: p^3*q*r and p^2*q^2*r. A074206(p^3*q*r) = 132 and A074206(p^2*q^2*r) = 176, so a(5, 3) = 132+176 = 308.


CROSSREFS

A035341 gives the row sums. Cf. A050324, A074206, A093936, A096443.
Sequence in context: A238975 A098348 A131420 * A034776 A068791 A219968
Adjacent sequences: A095702 A095703 A095704 * A095706 A095707 A095708


KEYWORD

nonn,tabl


AUTHOR

Alford Arnold, Jul 04 2004, Nov 22 2005


EXTENSIONS

Edited and extended by David Wasserman, Feb 22 2008


STATUS

approved



