A257997 - OEIS

A257997

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

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