A025674 -id:A025674 - cp's OEIS frontend

A025627 Numbers of form 6^i*8^j, with i, j >= 0.

1, 6, 8, 36, 48, 64, 216, 288, 384, 512, 1296, 1728, 2304, 3072, 4096, 7776, 10368, 13824, 18432, 24576, 32768, 46656, 62208, 82944, 110592, 147456, 196608, 262144, 279936, 373248, 497664, 663552, 884736, 1179648, 1572864, 1679616, 2097152

Offset: 1

David W. Wilson

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

Subsequence of A025610.

n = 10^6; Flatten[Table[6^i*8^j, {i, 0, Log[6, n]}, {j, 0, Log[8, n/6^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)

Sum_{n>=1} 1/a(n) = (6*8)/((6-1)*(8-1)) = 48/35. - Amiram Eldar, Sep 26 2020
a(n) ~ exp(sqrt(2*log(6)*log(8)*n)) / sqrt(48). - Vaclav Kotesovec, Sep 26 2020
a(n) = 6^A025661(n) * 8^A025674(n). - R. J. Mathar, Jul 06 2025

A025650 Exponent of 5 (value of j) in n-th number of form 4^i*5^j.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 7, 1, 2, 3, 4, 5, 6, 0, 7, 1, 8, 2, 3, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 11, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 11, 5, 12, 6, 0, 7, 1, 8, 2, 9

Offset: 1

David W. Wilson

nonn

Cf. A025617, A025646, A112765.

Differs from A025674 at a(1881).

With[{max = 10^10}, IntegerExponent[Sort[Flatten[Table[4^i*5^j, {i, 0, Log[4, max]}, {j, 0, Log[5, max/4^i]}]]], 5]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A112765(A025617(n)). - Amiram Eldar, Jul 09 2025

A025661 Exponent of 6 (value of i) in n-th number of form 6^i*8^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

Cf. A025627, A025674, A122841.

Differs from A025646 at a(1881).

With[{max = 10^12}, IntegerExponent[Sort[Flatten[Table[6^i*8^j, {i, 0, Log[6, max]}, {j, 0, Log[8, max/6^i]}]]], 6]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A122841(A025627(n)). - Amiram Eldar, Jul 09 2025

A025717 Index of 6^n within sequence of numbers of form 6^i*8^j.

Original entry on oeis.org

1, 2, 4, 7, 11, 16, 22, 29, 36, 44, 53, 63, 74, 86, 99, 112, 126, 141, 157, 174, 192, 211, 230, 250, 271, 293, 316, 340, 365, 390, 416, 443, 471, 500, 530, 561, 593, 625, 658, 692, 727, 763, 800, 838, 876, 915, 955, 996, 1038, 1081, 1125, 1169, 1214, 1260, 1307, 1355

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025674. - R. J. Mathar, Jul 06 2025

Differs from A025702 at a(65).

cp's OEIS Frontend

A025627 Numbers of form 6^i*8^j, with i, j >= 0.

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A025650 Exponent of 5 (value of j) in n-th number of form 4^i*5^j.

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A025661 Exponent of 6 (value of i) in n-th number of form 6^i*8^j.

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A025717 Index of 6^n within sequence of numbers of form 6^i*8^j.

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