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 A067003 Number of numbers <= n with same number of distinct prime factors as n. 8
 1, 1, 2, 3, 4, 1, 5, 6, 7, 2, 8, 3, 9, 4, 5, 10, 11, 6, 12, 7, 8, 9, 13, 10, 14, 11, 15, 12, 16, 1, 17, 18, 13, 14, 15, 16, 19, 17, 18, 19, 20, 2, 21, 20, 21, 22, 22, 23, 23, 24, 25, 26, 24, 27, 28, 29, 30, 31, 25, 3, 26, 32, 33, 27, 34, 4, 28, 35, 36, 5, 29, 37, 30, 38, 39, 40, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 FORMULA a(A002110(n)) = 1. EXAMPLE a(11)=8 since 2,3,4,5,7,8,9,11 each have one distinct prime factor. a(12)=3 since 6,10,12 each have two distinct prime factors. From Gus Wiseman, Dec 28 2018: (Start) Column n lists the a(n) positive integers less than or equal to n with the same number of distinct prime factors as n:   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20   ---------------------------------------------------------------------   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20         2  3  4     5  7  8  6   9   10  11  12  14  13  16  15  17  18            2  3     4  5  7      8   6   9   10  12  11  13  14  16  15               2     3  4  5      7       8   6   10  9   11  12  13  14                     2  3  4      5       7       6   8   9   10  11  12                        2  3      4       5           7   8   6   9   10                           2      3       4           5   7       8   6                                  2       3           4   5       7                                          2           3   4       5                                                      2   3       4                                                          2       3                                                                  2 (End) MATHEMATICA Table[Length[Select[Range[n], PrimeNu[#]==PrimeNu[n]&]], {n, 100}] (* Gus Wiseman, Dec 28 2018 *) PROG (PARI) a(n) = my(nb = #factor(n)~); sum(k=1, n, #factor(k)~ == nb); \\ Michel Marcus, Jul 13 2019 CROSSREFS Positions of 1's are A002110. Cf. A001221, A008479, A058933, A067004. Inverse of A000961, A007774, A033992, A033993, A051270 etc. Cf. A000010, A006049, A061142, A294277, A294278, A302242, A322837, A322841. Sequence in context: A133108 A055441 A104717 * A277884 A117386 A101174 Adjacent sequences:  A067000 A067001 A067002 * A067004 A067005 A067006 KEYWORD nonn,look AUTHOR Henry Bottomley, Dec 21 2001 STATUS approved

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Last modified October 17 15:32 EDT 2019. Contains 328116 sequences. (Running on oeis4.)