A025657 -id:A025657 - cp's OEIS frontend

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

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 *)

A025686 Exponent of 10 (value of j) in n-th number of form 4^i*10^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

Cf. A025621. Differs from A025657 at a(114). A025649 is the exponent of 4.

A025614 Numbers of form 3^i*6^j, with i, j >= 0.

Original entry on oeis.org

1, 3, 6, 9, 18, 27, 36, 54, 81, 108, 162, 216, 243, 324, 486, 648, 729, 972, 1296, 1458, 1944, 2187, 2916, 3888, 4374, 5832, 6561, 7776, 8748, 11664, 13122, 17496, 19683, 23328, 26244, 34992, 39366, 46656, 52488, 59049, 69984, 78732, 104976, 118098

Offset: 1

David W. Wilson

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

A025628 is a subsequence.
Cf. A003586, A003593, A003594, A003597, A107364.
Cf. A025610, A025618, A025622, A025626, A025627.

n = 10^6; Flatten[Table[3^i*6^j, {i, 0, Log[3, n]}, {j, 0, Log[6, n/3^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)

Sum_{n>=1} 1/a(n) = (3*6)/((3-1)*(6-1)) = 9/5. - Amiram Eldar, Sep 26 2020
a(n) ~ exp(sqrt(2*log(3)*log(6)*n)) / sqrt(18). - Vaclav Kotesovec, Sep 26 2020
a(n) = 3^A025641(n) *6^A025657(n). - R. J. Mathar, Jul 06 2025

A025697 Index of 3^n within sequence of numbers of form 3^i*6^j.

Original entry on oeis.org

1, 2, 4, 6, 9, 13, 17, 22, 27, 33, 40, 47, 55, 63, 72, 82, 92, 103, 115, 127, 140, 153, 167, 182, 197, 213, 229, 246, 264, 282, 301, 321, 341, 362, 383, 405, 428, 451, 475, 499, 524, 550, 576, 603, 630, 658, 687, 716, 746, 777, 808, 840, 872, 905, 939, 973, 1008, 1043

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025657. - R. J. Mathar, Jul 06 2025

cp's OEIS Frontend

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

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A025686 Exponent of 10 (value of j) in n-th number of form 4^i*10^j.

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A025614 Numbers of form 3^i*6^j, with i, j >= 0.

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A025697 Index of 3^n within sequence of numbers of form 3^i*6^j.

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