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.

A036451 Maximal value of d(x) (the number of divisors of x, A000005) if the binary order (see A029837) of x, the value g(x) = n.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 120, 144, 168, 200, 240, 288, 360, 432, 504, 600, 720, 864, 1008, 1152, 1344, 1600, 1920, 2304, 2688, 3072, 3584, 4096, 4800, 5760, 6720, 7680, 8640, 10080, 11520, 13824, 16128, 18432, 20736, 23040
Offset: 0

Views

Author

Labos Elemer

Keywords

Comments

g(x) <= n can be replaced by g(x) = n.

Examples

			In the range of g(x) <= 5, the values of d(x) can be: 1, 2, 3, 4, 5, 6, 8 of which 8 is the maximal, so a(n) = a(g(x)) = 8.

Links

Crossrefs

Cf. A000005, A002182, A029837, A005179, A007416, A036470-A036472.

Programs

  • Mathematica
    Max /@ Table[DivisorSigma[0, Floor[2^(n - 1) + k]], {n, 0, 22}, {k, Ceiling[2^(n - 1)]}] (* Michael De Vlieger, May 10 2017 *)

Extensions

a(22)-a(32) from Alex Ratushnyak, Jun 06 2013
a(33)-a(49) from Giovanni Resta, Jun 06 2013

A036484 a(n) is the minimal number of binary order n which has maximal number of divisors in this interval.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 60, 120, 240, 360, 840, 1680, 2520, 7560, 15120, 27720, 55440, 110880, 221760, 498960, 720720, 1441440, 3603600, 7207200, 14414400, 32432400, 61261200, 122522400, 245044800, 367567200, 735134400, 2095133040
Offset: 0

Views

Author

Labos Elemer

Keywords

Comments

Compare with A007416, where terms of this sequence are present.

Examples

			For n=9, with 256 < k <= 512, d(k) takes 17 distinct values, of which d(k)=24 is the greatest (see A036451 and A036470) and occurs first at k=360, so a(9)=360.

Crossrefs

Cf. A000005, A029837, A005179, A007416, A036470, A036492, A036493.

Programs

  • Mathematica
    Block[{nn = 22, s}, s = TakeList[Array[DivisorSigma[0, # + 1] &, 2^nn - 1], 2^Range[0, nn - 1]]; {1}~Join~Map[2^(#1 - 1) + #2 & @@ FirstPosition[s, #] &, Map[Max, s]]] (* Michael De Vlieger, Nov 04 2020 *)

Extensions

a(22)-a(31) from Sean A. Irvine, Nov 04 2020

A036493 Largest number having binary order n (A029837) and of which the number of divisors is maximal in that range of g(k) = n.

Original entry on oeis.org

1, 2, 4, 8, 12, 30, 60, 120, 240, 504, 840, 1680, 3960, 7560, 15120, 32760, 65520, 131040, 262080, 498960, 997920, 1965600, 3603600, 7207200, 14414400, 32432400, 64864800, 122522400, 245044800, 514594080, 1029188160, 2095133040, 4227022800, 8454045600
Offset: 0

Views

Author

Labos Elemer

Keywords

Comments

This sequence differs from A036451 only at n = 3, 5, 9, 12, and 15, which are the values of n for which there exists more than one k such that g(k) = n and d(k) has the maximum possible value.
a(n) is the largest term k in A067128 such that log_2(k) <= n. - Jon E. Schoenfield, May 13 2018

Examples

			For n = 9, k is in {257, 512}, max(d(k)) = 24 (see A036451); this holds for four different numbers (360, 420, 480, and 504); a(9) = 504 since it is the largest.

Crossrefs

Cf. A000005, A029837, A005179, A007416, A036451, A036470, A036484.

Programs

  • Mathematica
    {1}~Join~Table[Max@ MaximalBy[Range[2^(n - 1) + 1, 2^n], DivisorSigma[0, #] &], {n, 24}] (* Michael De Vlieger, Aug 01 2017 *)

Extensions

a(22)-a(24) from Michael De Vlieger, Aug 01 2017
a(25)-a(33) from Jon E. Schoenfield, May 12 2018
Showing 1-3 of 3 results.

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

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