OFFSET
1,2
COMMENTS
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
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 16 2015
STATUS
approved