A025647 -id:A025647 - cp's OEIS frontend

A025618 Numbers of form 4^i*6^j, with i, j >= 0.

1, 4, 6, 16, 24, 36, 64, 96, 144, 216, 256, 384, 576, 864, 1024, 1296, 1536, 2304, 3456, 4096, 5184, 6144, 7776, 9216, 13824, 16384, 20736, 24576, 31104, 36864, 46656, 55296, 65536, 82944, 98304, 124416, 147456, 186624, 221184, 262144, 279936

Offset: 1

David W. Wilson

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

Subsequence of A003586.

f[upto_]:=Module[{max4=Floor[Log[upto]/Log[4]],max6 = Floor[ Log[ upto]/ Log[6]], seq},seq=Union[4^First[#] 6^Last[#]&/@Tuples[ {Range[ 0,max4],Range[ 0,max6]}]];Select[seq,#<=upto&]];f[300000]  (* Harvey P. Dale, Mar 05 2011 *)

Sum_{n>=1} 1/a(n) = (4*6)/((4-1)*(6-1)) = 8/5. - Amiram Eldar, Sep 24 2020
a(n) ~ exp(sqrt(2*log(4)*log(6)*n)) / sqrt(24). - Vaclav Kotesovec, Sep 24 2020
a(n) = 4^A025647(n) * 6^A025658(n). - R. J. Mathar, Jul 06 2025

A025653 Exponent of 5 (value of i) in n-th number of form 5^i*8^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

Cf. A025623, A025673, A112765.

Differs from A025647 at a(2805).

With[{max = 10^11}, IntegerExponent[Sort[Flatten[Table[5^i*8^j, {i, 0, Log[5, max]}, {j, 0, Log[8, max/5^i]}]]], 5]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A112765(A025623(n)). - Amiram Eldar, Jul 09 2025

A025658 Exponent of 6 (value of j) in n-th number of form 4^i*6^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

Cf. A025618, A025647, A122841.

Differs from A025673 at a(2805).

With[{max = 10^10}, IntegerExponent[Sort[Flatten[Table[4^i*6^j, {i, 0, Log[4, max]}, {j, 0, Log[6, max/4^i]}]]], 6]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A122841(A025618(n)). - Amiram Eldar, Jul 09 2025

A025714 Index of 6^n within sequence of numbers of form 4^i*6^j.

Original entry on oeis.org

1, 3, 6, 10, 16, 23, 31, 41, 52, 64, 77, 92, 108, 125, 144, 164, 185, 207, 231, 256, 282, 310, 339, 369, 401, 434, 468, 503, 540, 578, 617, 658, 700, 743, 787, 833, 880, 928, 978, 1029, 1081, 1134, 1189, 1245, 1302, 1361, 1421, 1482, 1545, 1609, 1674, 1740, 1808

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025647. - R. J. Mathar, Jul 06 2025

Cf. A025618. Differs from A025729 at a(65).

a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=6, 4)); \\ Charles R Greathouse IV, Jan 16 2018

first(n)=my(s, N=1/6); vector(n+1, i, s+=logint(N*=6, 4)+1) \\ Charles R Greathouse IV, Jan 16 2018

cp's OEIS Frontend

A025618 Numbers of form 4^i*6^j, with i, j >= 0.

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A025653 Exponent of 5 (value of i) in n-th number of form 5^i*8^j.

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A025658 Exponent of 6 (value of j) in n-th number of form 4^i*6^j.

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A025714 Index of 6^n within sequence of numbers of form 4^i*6^j.

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