OFFSET
1,2
COMMENTS
Transpose of A286245.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 rows of triangle/antidiagonals of array
MathWorld, Pairing Function
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 (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
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 06 2017
STATUS
approved