cp's OEIS Frontend

A221645 Square array read by antidiagonals: T(n,k^2) = A040000(n) (= 1,2,2,2,...) if n=0 (mod k), T(n,k) = 0 else, n>=0, k>=1.

%I A221645 #20 Mar 13 2015 00:37:01
%S A221645 1,2,0,2,0,0,2,0,0,1,2,0,0,0,0,2,0,0,2,0,0,2,0,0,0,0,0,0,2,0,0,2,0,0,
%T A221645 0,0,2,0,0,0,0,0,0,0,1,2,0,0,2,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,2,0,
%U A221645 0,2,0,0,0,0,2,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0
%N A221645 Square array read by antidiagonals: T(n,k^2) = A040000(n) (= 1,2,2,2,...) if n=0 (mod k), T(n,k) = 0 else, n>=0, k>=1.
%C A221645 Other definition: Square array read by antidiagonal: T(n,k), n>=0, k>=1, in which column k lists the numbers A040000 (1, 2, 2, 2, 2...) interleaved with k^(1/2)-1 zeros, if k is a square otherwise column k lists only zeros.
%C A221645 The sum of elements of the n-th antidiagonal equals the number of divisors of n. In other words, the antidiagonal sums give A000005.
%F A221645 sum_{k=1...n} a(n-k,k) = A000005(n) for all n>0. - _M. F. Hasler_, Feb 02 2013
%e A221645 First 16 elements of first 16 rows of the square array are
%e A221645 1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,...
%e A221645 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,...
%e A221645 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,...
%e A221645 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,2,0,0,0,0,2,0,0,0,0,0,0,0,...
%e A221645 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,...
%e A221645 2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,...
%e A221645 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,2,0,0,0,0,2,0,0,0,0,0,0,2,...
%e A221645 2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,...
%e A221645 2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,...
%e A221645 ...
%e A221645 For n = 3 the sum of the third antidiagonal is 2+0+0 = d(3) = A000005(3) = 2.
%e A221645 For n = 16 the sum of the 16th antidiagonal is 2+0+0+2+0+0+0+0+0+0+0+0+0+0+0+1 = d(16) = A000005(16) = 5.
%o A221645 (PARI) A221645(n,m)={my(t); issquare(m,&t)||return; n||return(1); n%t & return;2} \\ _M. F. Hasler_, Feb 02 2013
%Y A221645 Cf. A000005, A212119.
%K A221645 nonn,tabl
%O A221645 1,2
%A A221645 _Omar E. Pol_, Feb 02 2013