

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
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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



