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.

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

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