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A060175 Table T(n,k) by antidiagonals of exponent of largest power of k-th prime which divides n. 7
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

Table of n, a(n) for n=1..120.

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-Fran├žois 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 August 5 22:11 EDT 2020. Contains 336214 sequences. (Running on oeis4.)