A025627 -id:A025627 - cp's OEIS frontend

A025629 Numbers of form 6^i*10^j with i, j >= 0.

1, 6, 10, 36, 60, 100, 216, 360, 600, 1000, 1296, 2160, 3600, 6000, 7776, 10000, 12960, 21600, 36000, 46656, 60000, 77760, 100000, 129600, 216000, 279936, 360000, 466560, 600000, 777600, 1000000, 1296000, 1679616, 2160000, 2799360, 3600000, 4665600

Offset: 1

David W. Wilson

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

Cf. A025610, A025618, A025622, A025626, A025627, A025628.

Cf. A025612, A025616, A025621, A025625, A025632, A025634.

n = 10^6; Flatten[Table[6^i*10^j, {i, 0, Log[6, n]}, {j, 0, Log10[n/6^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)

list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 10), N=10^n; while(N<=lim, listput(v, N); N*=6)); Set(v) \\ Charles R Greathouse IV, Jan 10 2018

Sum_{n>=1} 1/a(n) = (6*10)/((6-1)*(10-1)) = 4/3. - Amiram Eldar, Sep 26 2020
a(n) ~ exp(sqrt(2*log(6)*log(10)*n)) / sqrt(60). - Vaclav Kotesovec, Sep 26 2020
a(n) = 6^A025663(n) * 10^A025688(n). - R. J. Mathar, Jul 06 2025

A108698 Numbers of the form (6^i)*(11^j), with i, j >= 0.

Original entry on oeis.org

1, 6, 11, 36, 66, 121, 216, 396, 726, 1296, 1331, 2376, 4356, 7776, 7986, 14256, 14641, 26136, 46656, 47916, 85536, 87846, 156816, 161051, 279936, 287496, 513216, 527076, 940896, 966306, 1679616, 1724976, 1771561, 3079296, 3162456

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 19 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A025626, A025627, A025628, A025629, A064476, A107710, A003596, A003597, A107988, A003598, A108687, A003599, A107788, A108090.

import Data.Set (singleton, deleteFindMin, insert)
a108698 n = a108698_list !! (n-1)
a108698_list = f $ singleton (1,0,0) where
   f s = y : f (insert (6 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015

n = 10^6; Flatten[Table[6^i*11^j, {i, 0, Log[6, n]}, {j, 0, Log[11, n/6^i]}]] // Sort (* Amiram Eldar, Oct 07 2020 *)

Sum_{n>=1} 1/a(n) = (6*11)/((6-1)*(11-1)) = 33/25. - Amiram Eldar, Oct 07 2020

a(n) ~ exp(sqrt(2*log(6)*log(11)*n)) / sqrt(66). - Vaclav Kotesovec, Oct 07 2020

A025626 Numbers of form 6^i*7^j, with i, j >= 0.

Original entry on oeis.org

1, 6, 7, 36, 42, 49, 216, 252, 294, 343, 1296, 1512, 1764, 2058, 2401, 7776, 9072, 10584, 12348, 14406, 16807, 46656, 54432, 63504, 74088, 86436, 100842, 117649, 279936, 326592, 381024, 444528, 518616, 605052, 705894, 823543, 1679616, 1959552

Offset: 1

David W. Wilson

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

Cf. A025610, A025622, A025627, A025628, A025629.

Cf. A025619, A025631, A025632, A003591, A003594, A003595, A036566.

n = 10^6; Flatten[Table[6^i*7^j, {i, 0, Log[6, n]}, {j, 0, Log[7, n/6^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Sum_{n>=1} 1/a(n) = (6*7)/((6-1)*(7-1)) = 7/5. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(6)*log(7)*n)) / sqrt(42). - Vaclav Kotesovec, Sep 25 2020
a(n) = 6^A025660(n) * 7^A025668(n). - R. J. Mathar, Jul 06 2025

A107710 Numbers of the form (6^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 6, 13, 36, 78, 169, 216, 468, 1014, 1296, 2197, 2808, 6084, 7776, 13182, 16848, 28561, 36504, 46656, 79092, 101088, 171366, 219024, 279936, 371293, 474552, 606528, 1028196, 1314144, 1679616, 2227758, 2847312, 3639168, 4826809, 6169176

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 10 2005

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

Cf. A025626, A025627, A025628, A025629, A064476, A107326, A107364, A107462, A107466, A108056, A108090.

n = 10^6; Flatten[Table[6^i*13^j, {i, 0, Log[6, n]}, {j, 0, Log[13, n/6^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Sum_{n>=1} 1/a(n) = (6*13)/((6-1)*(13-1)) = 13/10. - Amiram Eldar, Sep 25 2020

a(n) ~ exp(sqrt(2*log(6)*log(13)*n)) / sqrt(78). - Vaclav Kotesovec, Sep 25 2020

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

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

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

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

A025629 Numbers of form 6^i*10^j with i, j >= 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A108698 Numbers of the form (6^i)*(11^j), with i, j >= 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Formula

A025626 Numbers of form 6^i*7^j, with i, j >= 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A107710 Numbers of the form (6^i)*(13^j), with i, j >= 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Crossrefs