login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle

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 xrange(1, 21): print [T(n, k) for k in xrange(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: A163510 A124735 A064874 * A216282 A147861 A167271

Adjacent sequences:  A286560 A286561 A286562 * A286564 A286565 A286566

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 20 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 19 08:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)