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A286244
Square array A(n,k) = P(A046523(k), floor((n+k-1)/k)), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), etc. Here P is a two-argument form of sequence A000027 used as a pairing function N x N -> N.
4
1, 3, 2, 3, 3, 4, 10, 3, 5, 7, 3, 10, 3, 5, 11, 21, 3, 10, 5, 8, 16, 3, 21, 3, 10, 5, 8, 22, 36, 3, 21, 3, 14, 5, 12, 29, 10, 36, 3, 21, 3, 14, 8, 12, 37, 21, 10, 36, 3, 21, 5, 14, 8, 17, 46, 3, 21, 10, 36, 3, 21, 5, 14, 8, 17, 56, 78, 3, 21, 10, 36, 3, 27, 5, 19, 12, 23, 67, 3, 78, 3, 21, 10, 36, 3, 27, 5, 19, 12, 23, 79
OFFSET
1,2
COMMENTS
Transpose of A286245.
EXAMPLE
The top left 12 X 12 corner of the array:
1, 3, 3, 10, 3, 21, 3, 36, 10, 21, 3, 78
2, 3, 3, 10, 3, 21, 3, 36, 10, 21, 3, 78
4, 5, 3, 10, 3, 21, 3, 36, 10, 21, 3, 78
7, 5, 5, 10, 3, 21, 3, 36, 10, 21, 3, 78
11, 8, 5, 14, 3, 21, 3, 36, 10, 21, 3, 78
16, 8, 5, 14, 5, 21, 3, 36, 10, 21, 3, 78
22, 12, 8, 14, 5, 27, 3, 36, 10, 21, 3, 78
29, 12, 8, 14, 5, 27, 5, 36, 10, 21, 3, 78
37, 17, 8, 19, 5, 27, 5, 44, 10, 21, 3, 78
46, 17, 12, 19, 5, 27, 5, 44, 14, 21, 3, 78
56, 23, 12, 19, 8, 27, 5, 44, 14, 27, 3, 78
67, 23, 12, 19, 8, 27, 5, 44, 14, 27, 5, 78
The first fifteen rows when viewed as a triangle:
1,
3, 2,
3, 3, 4,
10, 3, 5, 7,
3, 10, 3, 5, 11,
21, 3, 10, 5, 8, 16,
3, 21, 3, 10, 5, 8, 22,
36, 3, 21, 3, 14, 5, 12, 29,
10, 36, 3, 21, 3, 14, 8, 12, 37,
21, 10, 36, 3, 21, 5, 14, 8, 17, 46,
3, 21, 10, 36, 3, 21, 5, 14, 8, 17, 56,
78, 3, 21, 10, 36, 3, 27, 5, 19, 12, 23, 67,
3, 78, 3, 21, 10, 36, 3, 27, 5, 19, 12, 23, 79,
21, 3, 78, 3, 21, 10, 36, 5, 27, 5, 19, 12, 30, 92,
21, 21, 3, 78, 3, 21, 10, 36, 5, 27, 8, 19, 17, 30, 106
PROG
(Scheme)
(define (A286244 n) (A286244bi (A002260 n) (A004736 n)))
(define (A286244bi row col) (let ((a (A046523 col)) (b (quotient (+ row col -1) col))) (* (/ 1 2) (+ (expt (+ a b) 2) (- a) (- (* 3 b)) 2))))
(Python)
from sympy import factorint
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def P(n):
f = factorint(n)
return sorted([f[i] for i in f])
def a046523(n):
x=1
while True:
if P(n) == P(x): return x
else: x+=1
def A(n, k): return T(a046523(k), int((n + k - 1)/k))
for n in range(1, 21): print [A(k, n - k + 1) for k in range(1, n + 1)] # Indranil Ghosh, May 09 2017
CROSSREFS
Transpose: A286245.
Sequence in context: A111114 A242409 A317623 * A230010 A230847 A234300
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 06 2017
STATUS
approved