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

%I #26 Oct 27 2024 17:55:26

%S 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 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 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 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 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 T(n,k) = A027750(n, A000005(n) + 1 - k)/(A027750(n,k) - 1), 1 <= k <= A000005(n).

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 1;

%e 1, 3, 4, 1;

%e 1, 1;

%e 1, 4, 8, 1;

%e 1, 9, 1;

%e 1, 5, 16, 1;

%e 1, 1;

%e 1, 6, 16, 27, 32, 1.

%Y Cf. A000005 (row lengths), A027750, A087909 (row sums), A167401, A208239.

%K nonn,tabf

%O 1,7

%A _Gerasimov Sergey_, Mar 05 2013

%E a(83) corrected by _Jason Yuen_, Oct 27 2024