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.

User: Daniel Bishop

Daniel Bishop's wiki page.

Daniel Bishop has authored 3 sequences.

A244353 Largely composite numbers that are not highly composite.

Original entry on oeis.org

3, 8, 10, 18, 20, 30, 72, 84, 90, 96, 108, 168, 336, 420, 480, 504, 540, 600, 630, 660, 672, 1080, 1440, 2160, 3360, 3780, 3960, 4200, 4320, 4620, 4680, 9240, 12600, 13860, 18480, 30240, 32760, 36960, 37800, 40320, 41580, 42840, 43680, 65520, 75600, 98280, 131040, 138600, 151200, 163800, 196560, 262080, 327600, 360360, 393120, 415800, 443520, 471240, 480480, 491400, 655200, 831600, 942480, 982800, 997920
Offset: 1

Views

Author

Daniel Bishop, Jun 26 2014

Keywords

Links

Crossrefs

Equals A067128 excluding A002182.

Extensions

Wrong term 1 removed by J. Lowell, Feb 25 2019

A210618 Highly composite numbers (A002182) that lack a prime factor that the previous HCN has.

Original entry on oeis.org

45360, 43243200, 735134400, 2205403200, 73329656400, 97772875200, 146659312800, 293318625600, 13492656777600, 26985313555200, 391287046550400, 782574093100800, 4488062423933088000, 8976124847866176000, 184010559381256608000, 368021118762513216000
Offset: 1

Views

Author

Daniel Bishop, Mar 24 2012

Keywords

Examples

			The HCN 45360 is not a multiple of 11, but the previous HCN 27720 is.

Links

Crossrefs

Cf. A002182.

Extensions

Extended by T. D. Noe, Mar 26 2012

A210594 "Factor-dense" numbers: integers n where (# of proper divisors of n) / log(n) sets a new record.

Original entry on oeis.org

2, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160, 2882880, 3603600
Offset: 1

Views

Author

Daniel Bishop, Mar 23 2012

Keywords

Comments

Let d(n) = the number of proper divisors of n (A032741).
Define the "factor density" of n as f(n) = d(n) / log(n).
n is "factor dense" if f(m) < f(n) for all integers m where 2 <= m < n.
Missing highly-composite numbers (A002182) are 4 and 45360.
An alternative definition of factor density is g(n) = tau(n) / log(1+n), where tau(n) is the total number of divisors of n (A000005). Then records for g(n) appear to be set at all members of this sequence together with 1 and 4. - Hal M. Switkay, Sep 07 2022

Links

Crossrefs

Cf. A189686.

Programs

  • Mathematica
    f[n_] := N[(DivisorSigma[0, n] - 1)/Log[n]]; mx = 0; lst = {}; Do[ If[ f[n] > mx, mx = f[n]; AppendTo[lst, n]], {n, 2, 4000000, 2}]; t (* T. D. Noe, Mar 23 2012 *)
  • PARI
    lista(nn) = {my(m=0); for (n=2, nn, my(mm = (numdiv(n)-1)/log(n)); if (mm > m, print1(n, ", "); m = mm););} \\ Michel Marcus, Sep 08 2022

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

Content is available under The OEIS End-User License Agreement.