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 1-6 of 6 results.

A066150 Maximal number of divisors of any n-digit number.

Original entry on oeis.org

4, 12, 32, 64, 128, 240, 448, 768, 1344, 2304, 4032, 6720, 10752, 17280, 26880, 41472, 64512, 103680, 161280, 245760, 368640, 552960, 860160, 1290240, 1966080, 2764800, 4128768, 6193152, 8957952, 13271040, 19660800, 28311552, 41287680, 59719680, 88473600, 127401984, 181665792, 264241152, 382205952, 530841600
Offset: 1

Views

Author

Joseph L. Pe, Dec 12 2001

Keywords

Examples

			a(1) = 4 since 8 has 4 divisors and that is the record for 1-digit numbers.

Links

Crossrefs

Cf. A000005, A066151, A069650,
Cf. A130130 (minimal number of divisors of any n-digit number). [Jaroslav Krizek, Jul 18 2010]

Programs

  • PARI
    a066150(m,n) = local(d,a,k,b); for(d=m,n,a=0; for(k=10^d,10^(d+1)-1,b =numdiv(k); if(b>a,a=b)); print1(a,","))
a066150(0,6)

Formula

a(n) = largest integer m such that A005179(m) < 10^n. - Max Alekseyev, Apr 29 2010
a(n) = A000005(A066151(n)). - Amiram Eldar, Jul 02 2019

Extensions

One more term from Klaus Brockhaus, Dec 13 2001
Further terms from Vladeta Jovovic and Vladimir Baltic, Dec 16 2001
Extended further by David Wasserman, Jan 25 2002

A069650 Largest n-digit number with maximal number of divisors.

Original entry on oeis.org

8, 96, 840, 9240, 98280, 997920, 8648640, 99459360, 994593600, 9777287520, 97772875200, 963761198400, 9958865716800, 97821761637600, 978217616376000, 9651747148243200, 98930408269492800, 994651672331116800
Offset: 1

Views

Author

Amarnath Murthy, Apr 04 2002

Keywords

Crossrefs

Cf. A066150, A066151.

Extensions

Corrected by Ray Chandler, Jun 27 2004
a(8)-a(10) from Max Alekseyev, Apr 30 2010
a(11)-a(18) from Jon E. Schoenfield, May 11 2010

A091800 Largest n-digit number with maximal number of distinct prime divisors.

Original entry on oeis.org

6, 90, 990, 9870, 99330, 930930, 9699690, 99981420, 999068070, 9592993410, 99978788910, 999890501610, 9814524629910, 99999887777790, 999192361827660, 9999999768941490, 99992911041433410, 997799870344687410, 9999847102571786460, 99987077573596883670, 999999011467253427630, 9999928946485603635510
Offset: 1

Views

Author

Amarnath Murthy, Feb 21 2004

Keywords

Examples

			a(4) = 9870 as the largest number of distinct prime factors any 4-digit number can have and any number 9871 <= k <= 9999 has fewer than 5 prime factors. - _David A. Corneth_, Aug 19 2025

Links

Crossrefs

Cf. A000005, A002182, A002183, A066151, A074111.

Programs

  • Mathematica
    a[n_] := Module[{k=0, p=1, r=1, t=10^n}, While[r < t, p = NextPrime[p]; r *= p; k++]; k--; m = t-1; While[PrimeNu[m] != k, m--]; m]; Array[a, 8] (* Amiram Eldar, Mar 03 2020 *)
  • Python
    from sympy import nextprime, factorint
def A091800(n: int) -> int:
    k, p, r, t = 0, 1, 1, 10**n
    while r < t:
       p = nextprime(p)
       r *= p
       k += 1
    m = t - 1
    while len(factorint(m)) != k - 1: m -= 1
    return m # John Reimer Morales, Aug 18 2025
  • Python
    # see linked program

Extensions

Edited, corrected and extended by Ray Chandler, Feb 23 2004
a(10)-a(12) from Amiram Eldar, Mar 03 2020
a(13) from Giovanni Resta, Mar 04 2020
a(14) onwards from John Reimer Morales and David A. Corneth, Aug 19 2025

A120585 Smallest highly composite number(A002182) with n digits.

Original entry on oeis.org

1, 12, 120, 1260, 10080, 110880, 1081080, 10810800, 110270160, 1102701600, 10475665200, 128501493120, 1124388064800, 13492656777600, 130429015516800, 1010824870255200, 10108248702552000, 106858629141264000
Offset: 1

Views

Author

Lekraj Beedassy, Jun 16 2006

Keywords

Comments

Corresponds in fact to the {A112781(n-1) + 1}-th highly composite number. For the largest n-digit highly composite number {actually,A002182(A112781(n))}, see A066151.

Links

Crossrefs

Cf. A120586.

A240544 Table (read by rows) of all k-digit positive integers (in ascending order) with maximum number of divisors A066150(k).

Original entry on oeis.org

6, 8, 60, 72, 84, 90, 96, 840, 7560, 9240, 83160, 98280, 720720, 831600, 942480, 982800, 997920, 8648640, 73513440, 82162080, 86486400, 91891800, 98017920, 99459360, 735134400, 821620800, 931170240, 994593600, 6983776800, 8454045600, 9311702400, 9448639200, 9777287520, 97772875200, 963761198400
Offset: 1

Views

Author

Martin Renner, Apr 07 2014

Keywords

Comments

The number of elements in row k is A240543(k).

Examples

			The table T(k,m), m = 1..A240543(k), begins
6, 8;
60, 72, 84, 90, 96;
840;
etc.

Links

Crossrefs

Cf. A066151, A069650, A240543.

Extensions

a(29)-a(35) from Giovanni Resta, Apr 08 2014

A240543 Number of n-digit positive integers with maximum number of divisors A066150(n).

Original entry on oeis.org

2, 5, 1, 2, 2, 5, 1, 6, 4, 5, 1, 1, 2, 1, 2, 3, 7, 2
Offset: 1

Views

Author

Martin Renner, Apr 07 2014

Keywords

Examples

			a(1) = 2, since two 1-digit numbers have the maximum number of divisors 4 = #{1, 2, 3, 6} = #{1, 2, 4, 8}.
a(2) = 5, since five 2-digit numbers have the maximum number of divisors 12 = #{1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60} = #{1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72} = #{1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84} = #{1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90} = #{1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}.

Crossrefs

Cf. A066151, A069650, A240544.

Extensions

a(10)-a(12) from Giovanni Resta, Apr 08 2014
a(13)-a(18) from Kevin P. Thompson, Sep 04 2022
Showing 1-6 of 6 results.

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

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