OFFSET
1,10
EXAMPLE
a(12,1) = 2 since 4 = 2^2 = p_1^2 divides 12 but 8 = 2^3 does not.
a(12,2) = 1 since 3 = p_2 divides 12 but 9 = 3^2 does not.
See also examples in A249344, which is transpose of this array.
The top-left corner of the array:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
2, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...
...
MATHEMATICA
T[n_, k_] := IntegerExponent[n, Prime[k]];
Table[T[n-k+1, k], {n, 1, 15}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Nov 18 2019 *)
PROG
(Scheme)
(define (A249344bi row col) (let ((p (A000040 row))) (let loop ((n col) (i 0)) (cond ((not (zero? (modulo n p))) i) (else (loop (/ n p) (+ i 1)))))))
;; Antti Karttunen, Oct 28 2014
(Python)
from sympy import prime
def a(n, k):
p=prime(n)
i=z=0
while p**i<=k:
if k%(p**i)==0: z=i
i+=1
return z
for n in range(1, 10): print([a(n - k + 1, k) for k in range(1, n + 1)]) # Indranil Ghosh, Jun 24 2017
(PARI) a(n, k) = valuation(n, prime(k)); \\ Michel Marcus, Jun 24 2017
CROSSREFS
KEYWORD
AUTHOR
Henry Bottomley, Mar 14 2001
EXTENSIONS
Erroneous example corrected and more terms computed by Antti Karttunen, Oct 28 2014
STATUS
approved