A025641 -id:A025641 - cp's OEIS frontend

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

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

A025649 Exponent of 4 (value of i) in n-th number of form 4^i*10^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

Cf. A025621. Differs from A025641 at a(114). A025686 is exponent of 10.

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).

A025713 Index of 6^n within sequence of numbers of form 3^i*6^j.

Original entry on oeis.org

1, 3, 7, 12, 19, 28, 38, 50, 64, 79, 96, 114, 134, 156, 179, 204, 231, 259, 289, 320, 353, 388, 424, 462, 502, 543, 586, 631, 677, 725, 774, 825, 878, 932, 988, 1046, 1105, 1166, 1228, 1292, 1358, 1425, 1494, 1565, 1637, 1711, 1787, 1864, 1943, 2023, 2105, 2189

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025641. - R. J. Mathar, Jul 06 2025

cp's OEIS Frontend

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

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A025649 Exponent of 4 (value of i) in n-th number of form 4^i*10^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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A025713 Index of 6^n within sequence of numbers of form 3^i*6^j.

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