A392740 5-smooth numbers k = s(i) such that s(i)/s(i+1) sets a record high, where s = A051037.

1, 2, 3, 4, 5, 8, 9, 15, 24, 80, 2025, 15552, 32768, 274658203125, 7625597484987, 9007199254740992, 450283905890997363, 381469726562500000000000000000, 17763086495282268024161967871623168, 2922977339492680612451840826835216578535400390625

Offset

1,2

Comments

No larger terms for n <= s(78738133) = 2^1200.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..22

Example

Let facs(x) represent the standard form prime decomposition of x.
Table of n, a(n) = s(i) for n = 1..22:
 n         i     a(n)  facs(s(i))    facs(s(i+1))
-------------------------------------------------
 1         1       1   1             2
 2         2       2   2             3
 3         3       3   3             2^2
 4         4       4   2^2           5
 5         5       5   5             2 * 3
 6         7       8   2^3           3^2
 7         8       9   3^2           2 * 5
 8        11      15   3 * 5         2^4
 9        15      24   2^3 * 3       5^2
10        30      80   2^4 * 5       3^4
11       109    2025   3^4 * 5^2     2^11
12       197   15552   2^6 * 3^5     5^6
13       240   32768   2^15          3^8 * 5
14      2993           3^2 * 5^15    2^38
15      4190           3^27          2 * 5^18
16      7716           2^53          3^10 * 5^16
17     10322           3^37          2^54 * 5^2
18     46264           2^17 * 5^35   3^62
19     71093           2^90 * 3^15   5^49
20    197754           3^84 * 5^12   2^161
21   5105847           5^207         2^21  * 3^290
22   8629955           2^573         3^237 * 5^85

Mathematica

s = Block[{n = 2^60}, Union@ Flatten@ Table[2^i * 3^j * 5^k, {i, 0, Log[2, n]}, {j, 0, Log[3, n/2^i]}, {k, 0, Log[5, n/(2^i * 3^j)]} ] ]; Numerator@ Union@ FoldList[Max, Divide @@@ Partition[s, 2, 1] ]

Crossrefs

Cf. A051037, A085152, A392635, A392739.

Sequence in context: A354829 A393574 A085152 * A264886 A369294 A287117

Adjacent sequences: A392737 A392738 A392739 * A392741 A392742 A392743

Keyword

nonn

Author

Zhicheng Wei, Feb 25 2026

Status

approved