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Triangle A286239 reversed.
2

%I #11 Dec 07 2019 12:18:29

%S 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,

%T 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,

%U 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

%N Triangle A286239 reversed.

%C See A286239.

%H Antti Karttunen, <a href="/A286238/b286238.txt">Table of n, a(n) for n = 1..10585; the first 145 rows of triangle/antidiagonals of array</a>

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

%e The first fifteen rows of triangle:

%e 1,

%e 2, 1,

%e 4, 0, 3,

%e 7, 0, 2, 3,

%e 11, 0, 0, 0, 10,

%e 16, 0, 0, 4, 5, 3,

%e 22, 0, 0, 0, 0, 0, 21,

%e 29, 0, 0, 0, 7, 0, 5, 10,

%e 37, 0, 0, 0, 0, 0, 8, 0, 21,

%e 46, 0, 0, 0, 0, 11, 0, 0, 14, 10,

%e 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55,

%e 67, 0, 0, 0, 0, 0, 16, 0, 12, 8, 5, 10,

%e 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78,

%e 92, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 27, 21,

%e 106, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 19, 0, 36

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

%o (Python)

%o from sympy import totient

%o def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

%o def t(n, k): return 0 if n%k!=0 else T(totient(n/k), k)

%o for n in range(1, 21): print [t(n, k) for k in range(1, n + 1)][::-1] # _Indranil Ghosh_, May 09 2017

%Y Transpose: A286239 (triangle reversed).

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, May 06 2017