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 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 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

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