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 A037088 Triangle read by rows: T(n,k) is number of numbers x, 2^n <= x < 2^(n+1), with k prime factors (counted with multiplicity). 3
 2, 2, 2, 2, 4, 2, 5, 4, 5, 2, 7, 12, 6, 5, 2, 13, 20, 17, 7, 5, 2, 23, 40, 30, 20, 8, 5, 2, 43, 75, 65, 37, 21, 8, 5, 2, 75, 147, 131, 81, 41, 22, 8, 5, 2, 137, 285, 257, 173, 91, 44, 22, 8, 5, 2, 255, 535, 536, 344, 199, 96, 46, 22, 8, 5, 2, 464, 1062, 1033, 736, 403, 215, 99, 47 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence A092097 gives the limiting behavior at the end of the rows. - T. D. Noe, Feb 22 2008 LINKS T. D. Noe, Rows n=1..24 of triangle, flattened EXAMPLE The triangular array begins 2; 2,2; 2,4,2; 5,4,5,2; 7,12,6,5,2; ... a(7) = 5 because the 3-almost primes between 16 and 32 are (18,20,27,28,30). MATHEMATICA t[n_, k_] := Count[Range[2^n, 2^(n+1)-1], x_ /; Total[FactorInteger[x][[All, 2]]] == k]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 07 2013 *) CROSSREFS A001222 counts factors of n. A000040, A001358, A014612-A014614 are special cases. A036378 and A025488 are applications of binary order A029837. Leading diagonal is essentially A036378 and has partial sums A007053. Sequence in context: A089818 A067025 A049047 * A260722 A153436 A354359 Adjacent sequences: A037085 A037086 A037087 * A037089 A037090 A037091 KEYWORD nonn,tabl,nice AUTHOR Alford Arnold EXTENSIONS More terms from Naohiro Nomoto, Jun 18 2001 STATUS approved

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Last modified March 1 19:16 EST 2024. Contains 370443 sequences. (Running on oeis4.)