A025661 -id:A025661 - 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

A025646 Exponent of 4 (value of i) in n-th number of form 4^i*5^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. A025617, A025650, A235127.

Differs from A025661 at a(1881).

With[{nn=15},IntegerExponent[#,4]&/@Union[Flatten[Table[4^x 5^y,{x,0,nn},{y,0,nn}]]]] (* Harvey P. Dale, May 10 2019 *)
With[{max = 10^10}, IntegerExponent[Sort[Flatten[Table[4^i*5^j, {i, 0, Log[4, max]}, {j, 0, Log[5, max/4^i]}]]], 4]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A235127(A025617(n)). - Amiram Eldar, Jul 09 2025

A025674 Exponent of 8 (value of j) in n-th number of form 6^i*8^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. A025627, A025661, A244413.

Differs from A025650 at a(1881).

With[{max = 10^12}, SortBy[Flatten[Table[{i, j}, {i, 0, Log[6, max]}, {j, 0, Log[8, max/6^i]}], 1], 6^#[[1]] * 8^#[[2]] &][[;; , 2]]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A244413(A025627(n)/6^A025661(n)). - Amiram Eldar, Jul 09 2025

A025730 Index of 8^n within sequence of numbers of form 6^i*8^j.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 37, 47, 58, 70, 83, 97, 113, 130, 148, 167, 187, 208, 231, 255, 280, 306, 333, 361, 391, 422, 454, 487, 521, 556, 592, 630, 669, 709, 750, 792, 835, 880, 926, 973, 1021, 1070, 1120, 1172, 1225, 1279, 1334, 1390, 1447, 1506, 1566, 1627, 1689

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025661. - R. J. Mathar, Jul 06 2025

Cf. A001018, A025627.

Differs from A025706 at a(56).

cp's OEIS Frontend

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

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A025646 Exponent of 4 (value of i) in n-th number of form 4^i*5^j.

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A025674 Exponent of 8 (value of j) in n-th number of form 6^i*8^j.

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A025730 Index of 8^n within sequence of numbers of form 6^i*8^j.

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