A341435 Numbers k that are divisible by their product of digits in a record number of bases 1 < b < k.

1, 3, 6, 8, 12, 16, 24, 36, 48, 72, 96, 120, 144, 216, 288, 432, 576, 720, 864, 1080, 1152, 1440, 2016, 2160, 2880, 3600, 4320, 5040, 5760, 6480, 7200, 8640, 10080, 10800, 14400, 20160, 21600, 25920, 28800, 32400, 40320, 43200, 50400, 64800, 86400, 100800, 129600

Offset

1,2

Comments

The corresponding record values are 0, 1, 2, 3, 5, 6, 9, 12, 15, 20, 22, 23, 32, 35, 46, 52, 58, 68, 69, 71, 76, 95, 96, 106, 126, 137, 145, 149, 161, 164, 185, 191, 196, 218, 249, 266, 286, 290, 310, 318, 330, 375, 387, 428, 471, 510, 564, ...

It seems that most terms are least integers of a prime signature (A025487), but some are not: e.g., 3 and 2016.

Links

Table of n, a(n) for n=1..47.

Example

The values of A341434(k) for k=1..8 are 0, 0, 1, 1, 1, 2, 2, 3. The record values, 0, 1, 2 and 3, occur at 1, 3, 6 and 8, the first 4 terms of this sequence.

Mathematica

q[n_, b_] := (p = Times @@ IntegerDigits[n, b]) > 0 && Divisible[n, p]; a[n_] := Count[Range[2, n], _?(q[n, #] &)]; s = {}; am = -1; Do[a1 = a[n]; If[a1 > am, am = a1; AppendTo[s, n]], {n, 1, 10^3}]; s

Crossrefs

Indices of records in A341434.

Cf. A330813.

Sequence in context: A310138 A310139 A350619 * A301283 A288218 A212984

Adjacent sequences: A341432 A341433 A341434 * A341436 A341437 A341438

Keyword

nonn,base

Author

Amiram Eldar, Feb 11 2021

Status

approved