login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A343731 Numbers k at which tau(k^k) reaches a record high, where tau is the number-of-divisors function A000005. 1
0, 2, 3, 4, 6, 10, 12, 18, 20, 24, 30, 42, 60, 78, 84, 90, 114, 120, 140, 150, 156, 168, 180, 210, 330, 390, 420, 510, 546, 570, 630, 660, 780, 840, 990, 1020, 1050, 1092, 1140, 1170, 1260, 1530, 1540, 1560, 1680, 1848, 1890, 1980, 2100, 2280, 2310, 2730, 3570 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 510 terms from Chai Wah Wu)

EXAMPLE

In the table below, asterisks indicate record high values of tau(k^k):

                        tau(k^k) =

   k  k^k = A000312(k)  A062319(k)

  --  ----------------  ----------

   0                 1           1 *

   1                 1           1

   2                 4           3 *

   3                27           4 *

   4               256           9 *

   5              3125           6

   6             46656          49 *

   7            823543           8

   8          16777216          25

   9         387420489          19

  10       10000000000         121 *

  11      285311670611          12

  12     8916100448256         325 *

.

The numbers k at which those record high values occur are 0, 2, 3, 4, 5, 6, 10, 12, ...

PROG

(Python)

from functools import reduce

from operator import mul

from sympy import factorint

c, A343731_list = 0, [0]

for n in range(2, 10**5):

    x = reduce(mul, (n*d+1 for d in factorint(n).values()))

    if x > c:

        c = x

        A343731_list.append(n) # Chai Wah Wu, Jun 03 2021

CROSSREFS

Cf. A000005, A000312, A062319.

Sequence in context: A069744 A229362 A249685 * A181312 A330006 A288784

Adjacent sequences:  A343728 A343729 A343730 * A343732 A343733 A343734

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Jun 01 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 09:44 EDT 2021. Contains 347583 sequences. (Running on oeis4.)