A286562 Transpose of square array A286561.

1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 3, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset

1,12

Comments

See A286561 and A286563.

Links

Antti Karttunen, Table of n, a(n) for n = 1..7875; the first 125 antidiagonals of array

Example

The top left 16 X 16 corner of the array:
  n \ k
     \ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
     .-----------------------------------------------
   1 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
   2 | 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4
   3 | 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0
   4 | 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2
   5 | 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0
   6 | 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
   7 | 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0
   8 | 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
   9 | 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
  10 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
  11 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0
  12 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
  13 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
  14 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0
  15 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0
  16 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
The array is read by descending antidiagonals.

Prog

(Scheme) (define (A286562 n) (A286561bi (A004736 n) (A002260 n))) ;; For A286561bi see A286561.
(Python)
def a(n, k):
    i=1
    if k==1: return 1
    while n%(k**i)==0:
        i+=1
    return i-1
for n in range(1, 21): print [a(k, n - k + 1) for k in range(1, n + 1)][::-1] # Indranil Ghosh, May 20 2017

Crossrefs

Cf. A286561, A286563.

Sequence in context: A010110 A116905 A115079 * A185644 A319080 A025435

Adjacent sequences: A286559 A286560 A286561 * A286563 A286564 A286565

Keyword

nonn,tabl

Author

Antti Karttunen, May 20 2017

Status

approved