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A213919 Triangle read by rows: T(n,m) = (n/k)^(k-1), where k is the m-th divisor of n, 1 <= m <= tau(n).

%I A213919 #26 Oct 27 2024 17:55:26
%S A213919 1,1,1,1,1,1,2,1,1,1,1,3,4,1,1,1,1,4,8,1,1,9,1,1,5,16,1,1,1,1,6,16,27,
%T A213919 32,1,1,1,1,7,64,1,1,25,81,1,1,8,64,128,1,1,1,1,9,36,243,256,1,1,1,1,
%U A213919 10,125,256,512,1,1,49,729,1,1,11,1024,1,1,1,1,12,64,216,1024,2187,2048,1,1,625,1,1,13,4096,1,1,81,6561,1,1,14,343,4096
%N A213919 Triangle read by rows: T(n,m) = (n/k)^(k-1), where k is the m-th divisor of n, 1 <= m <= tau(n).
%C A213919 Divisor k of composite number n with maximal value (n/k)^(k-1): 2, 3, 4, 3, 5, 6, 7, 5, 8, 9, 10, 7, 11, 8, 5, 13, 9, 14,...
%F A213919 T(n,k) = A027750(n, A000005(n) + 1 - k)/(A027750(n,k) - 1), 1 <= k <= A000005(n).
%e A213919 Triangle begins:
%e A213919   1;
%e A213919   1, 1;
%e A213919   1, 1;
%e A213919   1, 2, 1;
%e A213919   1, 1;
%e A213919   1, 3, 4, 1;
%e A213919   1, 1;
%e A213919   1, 4, 8, 1;
%e A213919   1, 9, 1;
%e A213919   1, 5, 16, 1;
%e A213919   1, 1;
%e A213919   1, 6, 16, 27, 32, 1.
%Y A213919 Cf. A000005 (row lengths), A027750, A087909 (row sums), A167401, A208239.
%K A213919 nonn,tabf
%O A213919 1,7
%A A213919 _Gerasimov Sergey_, Mar 05 2013
%E A213919 a(83) corrected by _Jason Yuen_, Oct 27 2024