A025614 -id:A025614 - cp's OEIS frontend

A025628 Numbers of form 6^i*9^j, with i, j >= 0.

1, 6, 9, 36, 54, 81, 216, 324, 486, 729, 1296, 1944, 2916, 4374, 6561, 7776, 11664, 17496, 26244, 39366, 46656, 59049, 69984, 104976, 157464, 236196, 279936, 354294, 419904, 531441, 629856, 944784, 1417176, 1679616, 2125764, 2519424, 3188646

Offset: 1

David W. Wilson

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A025614.

n = 10^6; Flatten[Table[6^i*9^j, {i, 0, Log[6, n]}, {j, 0, Log[9, n/6^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)

Sum_{n>=1} 1/a(n) = (6*9)/((6-1)*(9-1)) = 27/20. - Amiram Eldar, Sep 26 2020
a(n) ~ exp(sqrt(2*log(6)*log(9)*n)) / sqrt(54). - Vaclav Kotesovec, Sep 26 2020
a(n) = 6^A025662(n) *9^A025680(n). - R. J. Mathar, Jul 06 2025

A025641 Exponent of 3 (value of i) in n-th number of form 3^i*6^j.

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 8, 0, 5, 2, 7, 4, 9, 1, 6, 3, 8, 0, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 0, 5, 10, 2, 7, 12, 4, 9, 14, 1, 6, 11, 3, 8, 13, 0, 5, 10, 15, 2, 7, 12, 4, 9, 14, 1, 6, 11, 16, 3, 8, 13, 0, 5, 10

Offset: 1

David W. Wilson

nonn

Also known as (exponent of 3 in n-th number of the form 3^i * 6^j) - (exponent of 2 in n-th number of the form 3^i * 6^j). - David A. Corneth, Jan 12 2021

			a(5) = 1 as the 5th number of the form 3^i * 6^j is 18 = 3^1 * 6^1 which has exponent of 3 equal to 1. - _David A. Corneth_, Jan 12 2021

David A. Corneth, Table of n, a(n) for n = 1..10000

Differs from A025649 at a(114). A025657 is exponent of 6.

Cf. A025614.

SortBy[Join @@ Table[{i, 3^i*6^j}, {i, 0, Log[3, #]}, {j, 0, Log[6, #/3^i]}], Last] &[10^8][[All, 1]] (* Michael De Vlieger, Jan 12 2021, after Amiram Eldar at A025614 *)

A025657 Exponent of 6 (value of j) in n-th number of form 3^i*6^j.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 2, 1, 0, 2, 1, 3, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 0, 5, 2, 4, 1, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 0, 8, 5, 2, 7, 4, 1, 6, 3, 0, 8, 5, 2, 7, 4, 1, 9, 6, 3, 0, 8, 5, 2, 7, 4, 1, 9, 6, 3, 0, 8, 5, 2, 10, 7, 4, 1, 9, 6, 3, 0, 8, 5, 2, 10

Offset: 1

David W. Wilson

nonn

Differs from A025686 at a(114). A025641 is the exponent of 3 (value of i).

Cf. A025614, A025641 (exponent of 3).

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A025628 Numbers of form 6^i*9^j, with i, j >= 0.

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A025641 Exponent of 3 (value of i) in n-th number of form 3^i*6^j.

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A025657 Exponent of 6 (value of j) in n-th number of form 3^i*6^j.

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