A286563 - OEIS

%I #29 Apr 28 2021 01:40:28

%S 1,1,1,1,0,1,1,2,0,1,1,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,1,3,0,1,0,0,

%T 0,1,1,0,2,0,0,0,0,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,2,

%U 1,1,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1

%N Triangular table T(n,k) read by rows: T(n,1) = 1, and for 1 < k <= n, T(n,k) = the highest exponent e such that k^e divides n.

%C T(n,k) > 0 for k in row n of A027750. - _Michael De Vlieger_, May 20 2017

%C Compare rows to those of triangle A279907, smallest exponent e of n divisible by k. The values of k > -1 in row n of A279907 pertain to k in row n of A162306 rather than k in row n of A027750. - _Michael De Vlieger_, May 21 2017

%H Antti Karttunen, <a href="/A286563/b286563.txt">Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle</a>

%F T(n,k) = A286561(n,k) listed row by row for n >= 1, k = 1 .. n.

%e The first fifteen rows of this triangular table:

%e   1,

%e   1, 1,

%e   1, 0, 1,

%e   1, 2, 0, 1,

%e   1, 0, 0, 0, 1,

%e   1, 1, 1, 0, 0, 1,

%e   1, 0, 0, 0, 0, 0, 1,

%e   1, 3, 0, 1, 0, 0, 0, 1,

%e   1, 0, 2, 0, 0, 0, 0, 0, 1,

%e   1, 1, 0, 0, 1, 0, 0, 0, 0, 1,

%e   1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

%e   1, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1,

%e   1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,

%e   1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,

%e   1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

%t Table[If[k == 1, 1, IntegerExponent[n, k]], {n, 15}, {k, n}] // Flatten (* _Michael De Vlieger_, May 20 2017 *)

%o (Scheme) (define (A286563 n) (A286561bi (A002024 n) (A002260 n))) ;; For A286561bi see A286561.

%o (Python)

%o def T(n, k):

%o     i=1

%o     if k==1: return 1

%o     while n%(k**i)==0:

%o         i+=1

%o     return i-1

%o for n in range(1, 21): print([T(n, k) for k in range(1, n + 1)]) # _Indranil Ghosh_, May 20 2017

%Y Lower triangular region of A286561.

%Y Cf. A286564 (same triangle reversed).

%Y Cf. A169594 (row sums).

%Y Cf. also arrays A051731, A286158, A027750, A279907, A280269.

%K nonn,tabl

%O 1,8

%A _Antti Karttunen_, May 20 2017