A025622 -id:A025622 - cp's OEIS frontend

A025715 Index of 6^n in A025622 (numbers of form 5^i*6^j).

1, 3, 6, 10, 15, 21, 28, 36, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 201, 223, 246, 270, 295, 321, 348, 376, 405, 436, 468, 501, 535, 570, 606, 643, 681, 720, 761, 803, 846, 890, 935, 981, 1028, 1076, 1125, 1176, 1228, 1281, 1335, 1390, 1446, 1503, 1561, 1621

Offset: 0

David W. Wilson

Positions of zeros in A025651. - R. J. Mathar, Jul 06 2025

David A. Corneth, Table of n, a(n) for n = 0..9999 (First 500 terms from Giovanni Resta)
W. Kuszmaul, Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations, arXiv preprint arXiv:1509.08216 [cs.DM], 2015.

Cf. A025622, A025707.

lista(nn) = {v = []; for (n=0, nn, for (m = 0, nn, v = vecsort(concat(v, 5^n*6^m),,8););); n=0; for (k=1, #v, vk = v[k]; if ((valuation(vk, 6)==n) && (valuation(vk, 5) == 0), if (vk > 5^(nn+1), return(), print1(k, ", "); n++);););} \\ Michel Marcus, Sep 28 2015

a(n) >= binomial(n+2, 2). - David A. Corneth, Jul 20 2017

Offset set to 0 by Michel Marcus, Sep 27 2015

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

Original entry on oeis.org

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

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

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

A108201 Numbers of the form (5^i)*(12^j), with i, j >= 0.

Original entry on oeis.org

1, 5, 12, 25, 60, 125, 144, 300, 625, 720, 1500, 1728, 3125, 3600, 7500, 8640, 15625, 18000, 20736, 37500, 43200, 78125, 90000, 103680, 187500, 216000, 248832, 390625, 450000, 518400, 937500, 1080000, 1244160, 1953125, 2250000, 2592000

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 15 2005

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

Cf. A025622, A003595, A025623, A025624, A025625, A003598, A107466, A064476.

Take[Union[5^First[#] 12^Last[#]&/@Tuples[Range[0,20],2]],50] (* Harvey P. Dale, Mar 23 2012 *)

Sum_{n>=1} 1/a(n) = 15/11. - Amiram Eldar, Mar 29 2025

A025651 Exponent of 5 (value of i) in n-th number of form 5^i*6^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, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 0, 9, 8, 7, 6, 5, 4, 3, 2, 11, 1, 10, 0, 9, 8, 7, 6, 5, 4, 3, 12, 2, 11, 1, 10, 0, 9, 8, 7, 6, 5, 4, 13, 3, 12, 2, 11, 1, 10, 0, 9, 8, 7, 6, 5, 14, 4

Offset: 1

David W. Wilson

nonn

Cf. A025622.

A025659 Exponent of 6 (value of j) in n-th number of form 5^i*6^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, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 9, 1, 2, 3, 4, 5, 6, 7, 8, 0, 9, 1, 10, 2, 3, 4, 5, 6, 7, 8, 0, 9, 1, 10, 2, 11, 3, 4, 5, 6, 7, 8, 0, 9, 1, 10, 2, 11, 3, 12, 4, 5, 6, 7, 8, 0, 9, 1, 10

Offset: 1

David W. Wilson

nonn

Cf. A025622.

cp's OEIS Frontend

A025715 Index of 6^n in A025622 (numbers of form 5^i*6^j).

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

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

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

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A108201 Numbers of the form (5^i)*(12^j), with i, j >= 0.

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A025651 Exponent of 5 (value of i) in n-th number of form 5^i*6^j.

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A025659 Exponent of 6 (value of j) in n-th number of form 5^i*6^j.

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