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 A060175 Table T(n,k) by antidiagonals of exponent of largest power of k-th prime which divides n. 6
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 LINKS FORMULA T(n, k) = log(A060176(n, k))/log(A000040(k)) = k-th digit from right of A054841(n). 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 (A060175 n) (A249344bi (A004736 n) (A002260 n))) (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 Transpose: A249344. Column 1: A007814. Column 2: A007949. Column 3: A112765. Column 4: A214411. Cf. also A002260, A004736, A054841, A060176, A085604, A090622, A115627, A249421, A249422. Sequence in context: A028629 A047751 A028706 * A321537 A218876 A028621 Adjacent sequences:  A060172 A060173 A060174 * A060176 A060177 A060178 KEYWORD easy,nonn,tabl AUTHOR Henry Bottomley, Mar 14 2001 EXTENSIONS Erroneous example corrected and more terms computed by Antti Karttunen, Oct 28 2014 STATUS approved

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Last modified February 22 23:44 EST 2020. Contains 332157 sequences. (Running on oeis4.)