A286238 Triangle A286239 reversed.

1, 2, 1, 4, 0, 3, 7, 0, 2, 3, 11, 0, 0, 0, 10, 16, 0, 0, 4, 5, 3, 22, 0, 0, 0, 0, 0, 21, 29, 0, 0, 0, 7, 0, 5, 10, 37, 0, 0, 0, 0, 0, 8, 0, 21, 46, 0, 0, 0, 0, 11, 0, 0, 14, 10, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 67, 0, 0, 0, 0, 0, 16, 0, 12, 8, 5, 10, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 92, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 27, 21, 106, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 19, 0, 36

Offset: 1

Author

Antti Karttunen, May 06 2017

Keywords

• nonn
• tabl

Comments

See A286239.

Examples

			The first fifteen rows of triangle:
    1,
    2, 1,
    4, 0, 3,
    7, 0, 2, 3,
   11, 0, 0, 0, 10,
   16, 0, 0, 4,  5, 3,
   22, 0, 0, 0,  0,  0, 21,
   29, 0, 0, 0,  7,  0,  5, 10,
   37, 0, 0, 0,  0,  0,  8,  0, 21,
   46, 0, 0, 0,  0, 11,  0,  0, 14, 10,
   56, 0, 0, 0,  0,  0,  0,  0,  0,  0, 55,
   67, 0, 0, 0,  0,  0, 16,  0, 12,  8,  5, 10,
   79, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0, 78,
   92, 0, 0, 0,  0,  0,  0, 22,  0,  0,  0,  0, 27, 21,
  106, 0, 0, 0,  0,  0,  0,  0,  0,  0, 17,  0, 19,  0, 36
		

Links

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

Crossrefs

Transpose: A286239 (triangle reversed).

Programs

Python

from sympy import totient
def T(n, m): return ((n + m)**2 - n - 3*m + 2)//2
def t(n, k): return 0 if n%k!=0 else T(totient(n//k), k)
for n in range(1, 21): print([t(n, k) for k in range(1, n + 1)][::-1]) # Indranil Ghosh, May 09 2017

Scheme

(define (A286238 n) (A286239tr (A002024 n) (A038722 n))) ;; For A286239tr see A286239.

Formula

T(n,k) = A286239(k,n).