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.
%I A343731 #26 Jul 21 2024 15:45:45
%S A343731 0,2,3,4,6,10,12,18,20,24,30,42,60,78,84,90,114,120,140,150,156,168,
%T A343731 180,210,330,390,420,510,546,570,630,660,780,840,990,1020,1050,1092,
%U A343731 1140,1170,1260,1530,1540,1560,1680,1848,1890,1980,2100,2280,2310,2730,3570
%N A343731 Numbers k at which tau(k^k) reaches a record high, where tau is the number-of-divisors function A000005.
%H A343731 Jon E. Schoenfield, <a href="/A343731/b343731.txt">Table of n, a(n) for n = 1..10000</a> (first 510 terms from Chai Wah Wu)
%e A343731 In the table below, asterisks indicate record high values of tau(k^k):
%e A343731 tau(k^k) =
%e A343731 k k^k = A000312(k) A062319(k)
%e A343731 -- ---------------- ----------
%e A343731 0 1 1 *
%e A343731 1 1 1
%e A343731 2 4 3 *
%e A343731 3 27 4 *
%e A343731 4 256 9 *
%e A343731 5 3125 6
%e A343731 6 46656 49 *
%e A343731 7 823543 8
%e A343731 8 16777216 25
%e A343731 9 387420489 19
%e A343731 10 10000000000 121 *
%e A343731 11 285311670611 12
%e A343731 12 8916100448256 325 *
%e A343731 .
%e A343731 The numbers k at which those record high values occur are 0, 2, 3, 4, 5, 6, 10, 12, ...
%t A343731 Join[{0},DeleteDuplicates[Table[{n,DivisorSigma[0,n^n]},{n,2,3600}],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]]] (* _Harvey P. Dale_, Jul 21 2024 *)
%o A343731 (Python)
%o A343731 from functools import reduce
%o A343731 from operator import mul
%o A343731 from sympy import factorint
%o A343731 c, A343731_list = 0, [0]
%o A343731 for n in range(2,10**5):
%o A343731 x = reduce(mul,(n*d+1 for d in factorint(n).values()))
%o A343731 if x > c:
%o A343731 c = x
%o A343731 A343731_list.append(n) # _Chai Wah Wu_, Jun 03 2021
%Y A343731 Cf. A000005, A000312, A062319.
%K A343731 nonn
%O A343731 1,2
%A A343731 _Jon E. Schoenfield_, Jun 01 2021