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 A257997 Numbers of the form (2^i)*(3^j) or (2^i)*(5^j) or (3^i)*(5^j). 6
 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 32, 36, 40, 45, 48, 50, 54, 64, 72, 75, 80, 81, 96, 100, 108, 125, 128, 135, 144, 160, 162, 192, 200, 216, 225, 243, 250, 256, 288, 320, 324, 375, 384, 400, 405, 432, 486, 500, 512, 576, 625, 640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Union of A003586, A003592 and A003593. Subsequence of 5-smooth numbers (cf. A051037), having no more than two distinct prime factors: A006530(a(n)) <= 5; A001221(a(n)) <= 2. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Vaclav Kotesovec, Graph - the asymptotic ratio (80000000 terms) FORMULA a(n) ~ exp(sqrt(2*log(2)*log(3)*log(5)*n/log(30))). - Vaclav Kotesovec, Sep 22 2020 Sum_{n>=1} 1/a(n) = 29/8. - Amiram Eldar, Sep 23 2020 EXAMPLE . ----+------+---------     ----+------+----------- .   1 |   1  |  1            16 |  25  |  5^2 .   2 |   2  |  2            17 |  27  |  3^3 .   3 |   3  |  3            18 |  32  |  2^5 .   4 |   4  |  2^2          19 |  36  |  2^2 * 3^2 .   5 |   5  |  5            20 |  40  |  2^3 * 5 .   6 |   6  |  2 * 3        21 |  45  |  3^2 * 5 .   7 |   8  |  2^3          22 |  48  |  2^4 * 3 .   8 |   9  |  3^2          23 |  50  |  2 * 5^2 .   9 |  10  |  2 * 5        24 |  54  |  2 * 3^3 .  10 |  12  |  2^2 * 3      25 |  64  |  2^6 .  11 |  15  |  3 * 5        26 |  72  |  2^3 * 3^2 .  12 |  16  |  2^4          27 |  75  |  3 * 5^2 .  13 |  18  |  2 * 3^2      28 |  80  |  2^4 * 5 .  14 |  20  |  2^2 * 5      29 |  81  |  3^4 .  15 |  24  |  2^3 * 3      30 |  96  |  2^5 * 3 MATHEMATICA n = 1000; Join[Table[2^i*3^j, {i, 0, Log[2, n]}, {j, 0, Log[3, n/2^i]}], Table[3^i*5^j, {i, 0, Log[3, n]}, {j, 0, Log[5, n/3^i]}], Table[2^i*5^j, {i, 0, Log[2, n]}, {j, 0, Log[5, n/2^i]}]] // Flatten // Union (* Amiram Eldar, Sep 23 2020 *) PROG (Haskell) import Data.List.Ordered (unionAll) a257997 n = a257997_list !! (n-1) a257997_list = unionAll [a003586_list, a003592_list, a003593_list] CROSSREFS Cf. A003586, A003592, A003593, A051037, A006530, A001221, A258023 (subsequence). Cf. A337800, A337801. Sequence in context: A051661 A051037 A250089 * A070023 A035303 A291719 Adjacent sequences:  A257994 A257995 A257996 * A257998 A257999 A258000 KEYWORD nonn,easy AUTHOR Reinhard Zumkeller, May 16 2015 STATUS approved

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Last modified May 9 06:14 EDT 2021. Contains 343692 sequences. (Running on oeis4.)