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A286562 Transpose of square array A286561.

%I A286562 #16 Jun 10 2025 13:54:12
%S A286562 1,1,0,1,1,0,1,0,0,0,1,2,1,0,0,1,0,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0,
%T A286562 0,0,1,3,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,2,1,0,1,0,0,0,0,0,1,0,
%U A286562 0,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0
%N A286562 Transpose of square array A286561.
%C A286562 See A286561 and A286563.
%H A286562 Antti Karttunen, <a href="/A286562/b286562.txt">Table of n, a(n) for n = 1..7875; the first 125 antidiagonals of array</a>
%e A286562 The top left 16 X 16 corner of the array:
%e A286562   n \ k
%e A286562      \ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
%e A286562      .-----------------------------------------------
%e A286562    1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A286562    2 | 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4
%e A286562    3 | 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0
%e A286562    4 | 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2
%e A286562    5 | 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0
%e A286562    6 | 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
%e A286562    7 | 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0
%e A286562    8 | 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
%e A286562    9 | 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
%e A286562   10 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
%e A286562   11 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0
%e A286562   12 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
%e A286562   13 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
%e A286562   14 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0
%e A286562   15 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
%e A286562   16 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
%e A286562 The array is read by descending antidiagonals.
%o A286562 (Scheme) (define (A286562 n) (A286561bi (A004736 n) (A002260 n))) ;; For A286561bi see A286561.
%o A286562 (Python)
%o A286562 def a(n, k):
%o A286562     i=1
%o A286562     if k==1: return 1
%o A286562     while n%(k**i)==0:
%o A286562         i+=1
%o A286562     return i-1
%o A286562 for n in range(1, 21): print([a(k, n - k + 1) for k in range(1, n + 1)][::-1]) # _Indranil Ghosh_, May 20 2017
%Y A286562 Cf. A286561, A286563.
%K A286562 nonn,tabl
%O A286562 1,12
%A A286562 _Antti Karttunen_, May 20 2017