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A214845 Triangle read by rows: T(n,m) =(n/k)^(k-1) mod k, where k is the m-th divisor of n, 1 <= m <= tau(n).

%I A214845 #18 Apr 17 2013 16:39:19
%S A214845 0,0,1,0,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,1,0,0,1,3,2,
%T A214845 1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,3,4,1,0,1,0,0,1,1,2,1,0,1,
%U A214845 1,1,0,1,1,1,0,1,0,0,1,0,4,3,8,1,0,0,1,0,1,1,1,0,0,0,1,0,0,3,1,2,1,0,1,0,1,1,1,5,3,4,1
%N A214845 Triangle read by rows: T(n,m) =(n/k)^(k-1) mod k, where k is the m-th divisor of n, 1 <= m <= tau(n).
%C A214845 Row lengths are tau(n) = A000005(n).
%C A214845 The sequence of row sums starts: 0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 7, 1, 3, 3, 1, 1, 9, 1, 5, 3, 3, 1, 17, 1, 3, 1, 7, 1, 16, 1, 1, 3, 3, 3, 26, 1, 3, 3, 19, 1, 12, 1, 7, 18, 3, 1, 27, 1, 23...
%e A214845 Triangle begins:
%e A214845 0;
%e A214845 0,1;
%e A214845 0,1;
%e A214845 0,0,1;
%e A214845 0,1;
%e A214845 0,1,1,1;
%e A214845 0,1;
%e A214845 0,0,0,1;
%e A214845 0,0,1;
%e A214845 0,1,1,1;
%e A214845 0,1;
%e A214845 0,0,1,3,2,1;
%e A214845 0,1;
%e A214845 0,1,1,1;
%e A214845 0,1,1,1;
%e A214845 0,0,0,0,1;
%e A214845 0,1;
%e A214845 0,1,0,3,4,1;
%p A214845 A214845 := proc(n,m)
%p A214845     sort(convert(numtheory[divisors](n),list)) ;
%p A214845     k := op(m,%) ;
%p A214845     modp((n/k)^(k-1),k) ;
%p A214845 end proc:
%p A214845 for n from 1 to 30 do
%p A214845     for m from 1 to numtheory[tau](n) do
%p A214845         printf("%d,",A214845(n,m)) ;
%p A214845     end do:
%p A214845     printf("\n") ;
%p A214845 end do: # _R. J. Mathar_, Apr 17 2013
%Y A214845 Cf. A000005, A027750, A055225, A087909, A213919.
%K A214845 nonn,tabf,less
%O A214845 1,33
%A A214845 _Gerasimov Sergey_, Mar 08 2013