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%I #36 Mar 27 2021 22:47:39
%S 0,0,1,0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,
%T 0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,1,0,2,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
%N Table T(n,k) by antidiagonals of exponent of largest power of k-th prime which divides n.
%F T(n, k) = log(A060176(n, k))/log(A000040(k)) = k-th digit from right of A054841(n).
%e a(12,1) = 2 since 4 = 2^2 = p_1^2 divides 12 but 8 = 2^3 does not.
%e a(12,2) = 1 since 3 = p_2 divides 12 but 9 = 3^2 does not.
%e See also examples in A249344, which is transpose of this array.
%e The top-left corner of the array:
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...
%e ...
%t T[n_, k_] := IntegerExponent[n, Prime[k]];
%t Table[T[n-k+1, k], {n, 1, 15}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Nov 18 2019 *)
%o (Scheme)
%o (define (A060175 n) (A249344bi (A004736 n) (A002260 n)))
%o (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)))))))
%o ;; _Antti Karttunen_, Oct 28 2014
%o (Python)
%o from sympy import prime
%o def a(n, k):
%o p=prime(n)
%o i=z=0
%o while p**i<=k:
%o if k%(p**i)==0: z=i
%o i+=1
%o return z
%o for n in range(1, 10): print([a(n - k + 1, k) for k in range(1, n + 1)]) # _Indranil Ghosh_, Jun 24 2017
%o (PARI) a(n, k) = valuation(n, prime(k)); \\ _Michel Marcus_, Jun 24 2017
%Y Transpose: A249344.
%Y Column 1: A007814.
%Y Column 2: A007949.
%Y Column 3: A112765.
%Y Column 4: A214411.
%Y Cf. also A002260, A004736, A054841, A060176, A085604, A090622, A115627, A249421, A249422.
%K easy,nonn,tabl
%O 1,10
%A _Henry Bottomley_, Mar 14 2001
%E Erroneous example corrected and more terms computed by _Antti Karttunen_, Oct 28 2014
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