A258023 - OEIS

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A258023

Numbers of form (2^i)*(3^j) or (3^i)*(5^j).

1, 2, 3, 4, 5, 6, 8, 9, 12, 15, 16, 18, 24, 25, 27, 32, 36, 45, 48, 54, 64, 72, 75, 81, 96, 108, 125, 128, 135, 144, 162, 192, 216, 225, 243, 256, 288, 324, 375, 384, 405, 432, 486, 512, 576, 625, 648, 675, 729, 768, 864, 972, 1024, 1125, 1152, 1215, 1296

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Union of A003586 and A003593;

A006530(a(n)) <= 5; A001221(a(n)) <= 2; a(n) mod 10 != 0.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Graph - the asymptotic ratio (65000000 terms)

FORMULA

a(n) ~ exp(sqrt(2*log(2)*log(3)*log(5)*n / log(10))) / sqrt(3). - Vaclav Kotesovec, Sep 22 2020

Sum_{n>=1} 1/a(n) = 27/8. - Amiram Eldar, Sep 23 2020

EXAMPLE

. n | a(n) | n | a(n) |

. ----+-------+---------- ----+-------+------------

. 1 | 1 | 1 16 | 32 | 2^5

. 2 | 2 | 2 17 | 36 | 2^2 * 3^2

. 3 | 3 | 3 18 | 45 | 3^2 * 5

. 4 | 4 | 2^2 19 | 48 | 2^4 * 3

. 5 | 5 | 5 20 | 54 | 2 * 3^3

. 6 | 6 | 2 * 3 21 | 64 | 2^6

. 7 | 8 | 2^3 22 | 72 | 2^3 * 3^2

. 8 | 9 | 3^2 23 | 75 | 3 * 5^2

. 9 | 12 | 2^2 * 3 24 | 81 | 3^4

. 10 | 15 | 3 * 5 25 | 96 | 2^5 * 3

. 11 | 16 | 2^4 26 | 108 | 2^2 * 3^3

. 12 | 18 | 2 * 3^2 27 | 125 | 5^3

. 13 | 24 | 2^3 * 3 28 | 128 | 2^7

. 14 | 25 | 5^2 29 | 135 | 3^3 * 5

. 15 | 27 | 3^3 30 | 144 | 2^4 * 3^2

MATHEMATICA

n = 10^4; 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]}]] // Flatten // Union (* Amiram Eldar, Sep 23 2020 *)

PROG

(Haskell)

import Data.List.Ordered (union)

a258023 n = a258023_list !! (n-1)

a258023_list = union a003586_list a003593_list

CROSSREFS

Cf. A003586, A003593, A051037, A006530, A001221, A010879, subsequence of: A051037, A257997, A337800, A337801.

Sequence in context: A129525 A351987 A295165 * A190232 A377338 A084693

Adjacent sequences: A258020 A258021 A258022 * A258024 A258025 A258026

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, May 16 2015

STATUS

approved