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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Amiram Eldar, Feb 11 2021

Keywords

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.

Examples

			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.

Crossrefs

Indices of records in A341434.
Cf. A330813.

Programs

  • 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
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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