cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A333952 Recursively highly composite numbers: numbers m such that A067824(m) > A067824(k) for all k < m.

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 24, 36, 48, 72, 96, 120, 144, 192, 240, 288, 360, 432, 480, 576, 720, 864, 960, 1152, 1440, 1728, 1920, 2160, 2304, 2880, 3456, 4320, 5760, 6912, 8640, 11520, 17280, 23040, 25920, 30240, 34560, 46080, 51840, 60480, 69120, 86400, 103680, 120960
Offset: 1

Views

Author

Amiram Eldar, Apr 11 2020

Keywords

Comments

This sequence is not to be confused with A333931.
The corresponding record values are 1, 2, 4, 6, 8, 16, 40, 52, 96, ...
Fink (2019) defined this sequence. He asked whether 720 is the largest term that is also highly composite number (A002182).
This is, except the terms 2, the sequence records of indices of A074206 for positive n as a(n) = 2*A074206(n), n>1, i.e. A307866. (formula from - Vladeta Jovovic, Jul 03 2005) - David A. Corneth, Apr 13 2020

Examples

			The first 6 terms of A067824 are 1, 2, 2, 4, 2, 6. The record values occur at 1, 2, 4, 6, the first 4 terms of this sequence.

Links

Crossrefs

Cf. A002182, A067824, A307866, A333953.

Programs

  • Mathematica
    d[1] = 1; d[n_] := d[n] = 1 + DivisorSum[n, d[#] &, # < n &]; seq={}; dm = 0; Do[d1 = d[n]; If[d1 > dm, dm = d1; AppendTo[seq, n]], {n, 1, 10^4}]; seq

A353899 Indices of records in A353898.

Original entry on oeis.org

1, 2, 4, 6, 12, 30, 36, 60, 180, 420, 900, 1260, 4620, 6300, 13860, 44100, 55440, 69300, 180180, 485100, 720720, 900900, 3063060, 6306300, 12252240, 15315300, 58198140, 107207100, 232792560, 290990700, 1163962800, 2036934900, 5354228880, 6692786100, 22406283900
Offset: 1

Views

Author

Amiram Eldar, May 10 2022

Keywords

Comments

First differs from A333931 at n=23.
The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 48, 54, 72, 81, 96, 108, 144, 162, ... (see the link for more values).

Links

Crossrefs

Cf. A333931, A353898.
Subsequence of A025487 and A138302.
Similar sequences: A002182, A002110 (unitary), A037992 (infinitary), A293185, A306736, A307845, A309141, A318278, A322484, A335386.

Programs

  • Mathematica
    f[p_, e_] := Floor[Log2[e]] + 2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; seq = {}; sm = 0; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^6}]; seq

A377139 Numbers that have more cubefree divisors than any smaller number.

Original entry on oeis.org

1, 2, 4, 6, 12, 30, 36, 60, 180, 420, 900, 1260, 4620, 6300, 13860, 44100, 60060, 69300, 180180, 485100, 900900, 3063060, 6306300, 15315300, 58198140, 107207100, 290990700, 1179278100, 1338557220, 2036934900, 6692786100, 22406283900, 38818159380, 46849502700, 194090796900
Offset: 1

Views

Author

Amiram Eldar, Oct 17 2024

Keywords

Comments

First differ from A333931 and A353899 at n = 17.
Indices of records in A073184.
The corresponding record values are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 48, 54, 72, 81, 96, 108, ... (see the link for more values).

Links

Crossrefs

Subsequence of A004709 and A025487.
Cf. A004709, A073184, A333931, A353899, A377140.

Programs

  • Mathematica
    f[p_, e_] := If[e == 1, 2, 3]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n]; With[{v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]}, seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq]
Showing 1-3 of 3 results.

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

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