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A286563
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.
8
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, 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, 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
OFFSET
1,8
COMMENTS
T(n,k) > 0 for k in row n of A027750. - Michael De Vlieger, May 20 2017
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
FORMULA
T(n,k) = A286561(n,k) listed row by row for n >= 1, k = 1 .. n.
EXAMPLE
The first fifteen rows of this triangular table:
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, 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, 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
MATHEMATICA
Table[If[k == 1, 1, IntegerExponent[n, k]], {n, 15}, {k, n}] // Flatten (* Michael De Vlieger, May 20 2017 *)
PROG
(Scheme) (define (A286563 n) (A286561bi (A002024 n) (A002260 n))) ;; For A286561bi see A286561.
(Python)
def T(n, k):
i=1
if k==1: return 1
while n%(k**i)==0:
i+=1
return i-1
for n in range(1, 21): print([T(n, k) for k in range(1, n + 1)]) # Indranil Ghosh, May 20 2017
CROSSREFS
Lower triangular region of A286561.
Cf. A286564 (same triangle reversed).
Cf. A169594 (row sums).
Cf. also arrays A051731, A286158, A027750, A279907, A280269.
Sequence in context: A124735 A375202 A064874 * A216282 A147861 A167271
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 20 2017
STATUS
approved