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A263098 a(n) = Max( tau(k) : k=1,2,3,...,n^2 ) where tau(k) = A000005(k) is the number of divisors of k.

%I A263098 #14 Oct 11 2015 10:59:17
%S A263098 1,3,4,6,8,9,10,12,12,12,16,16,16,18,18,20,20,20,24,24,24,24,24,24,24,
%T A263098 24,30,30,32,32,32,32,32,32,32,36,36,36,36,36,40,40,40,40,40,40,40,40,
%U A263098 40,40,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,64,64,64,64,64,64,64,64,64,64,64,64,64,64,72
%N A263098 a(n) = Max( tau(k) : k=1,2,3,...,n^2 ) where tau(k) = A000005(k) is the number of divisors of k.
%H A263098 Antti Karttunen, <a href="/A263098/b263098.txt">Table of n, a(n) for n = 1..2080</a>
%F A263098 a(n) = A070319(A000290(n)).
%t A263098 Table[Max[DivisorSigma[0, #] & /@ Range[n^2]], {n, 101}] (* _Michael De Vlieger_, Oct 11 2015 *)
%o A263098 (PARI)
%o A263098 A070319(n, m=1, s=2)={for(k=s, n, m<numdiv(k)&m=numdiv(k)); m}; \\ This function from _M. F. Hasler_, Sep 12 2012
%o A263098 A263098 = n -> A070319(n^2); \\ Slow without memoization.
%o A263098 for(n=1, 2080, write("b263098.txt", n, " ", A263098(n)));
%o A263098 (Scheme) (define (A263098 n) (A070319 (A000290 n)))
%Y A263098 Cf. A000290, A070319, A262514.
%Y A263098 Cf. A263096, A263097.
%K A263098 nonn
%O A263098 1,2
%A A263098 _Antti Karttunen_, Oct 10 2015