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

1,2

Comments

See A286239.

Links

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

Formula

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

Example

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

Prog

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

Crossrefs

Transpose: A286239 (triangle reversed).

Sequence in context: A277994 A334112 A355625 * A286237 A059781 A233905

Adjacent sequences: A286235 A286236 A286237 * A286239 A286240 A286241

Keyword

nonn,tabl

Author

Antti Karttunen, May 06 2017

Status

approved