login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A341435 Numbers k that are divisible by their product of digits in a record number of bases 1 < b < k. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A220001 A310138 A310139 * A301283 A288218 A212984

Adjacent sequences:  A341432 A341433 A341434 * A341436 A341437 A341438

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Feb 11 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 18:28 EDT 2021. Contains 345419 sequences. (Running on oeis4.)