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 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A093936 is an analogous array for unordered factorizations. First column is A000079. First two diagonals are A000670 and A005649. LINKS 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

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Last modified December 5 12:42 EST 2022. Contains 358586 sequences. (Running on oeis4.)