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A290125 Square array read by antidiagonals T(n,k) = sigma(k + n) - sigma(k) - n, with n>=0 and k>=1. 1
0, 0, 1, 0, 0, 1, 0, 2, 2, 3, 0, -2, 0, 0, 1, 0, 5, 3, 5, 5, 6, 0, -5, 0, -2, 0, 0, 1, 0, 6, 1, 6, 4, 6, 6, 7, 0, -3, 3, -2, 3, 1, 3, 3, 4, 0, 4, 1, 7, 2, 7, 5, 7, 7, 8, 0, -7, -3, -6, 0, -5, 0, -2, 0, 0, 1, 0, 15, 8, 12, 9, 15, 10, 15, 13, 15, 15, 16 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
A015886(n) gives the position of the first zero in the n-th row of this array.
LINKS
FORMULA
T(0, k) = 0 for all k.
EXAMPLE
Array begins:
0, 0, 0, 0, 0, 0, 0, ...
1, 0, 2, -2, 5, -5, 6, ...
1, 2, 0, 3, 0, 1, 3, ...
3, 0, 5, -2, 6, -2, 7, ...
1, 5, 0, 4, 3, 2, 0, ...
6, 0, 6, 1, 7, -5, 15, ...
1, 6, 3, 5, 0, 10, 0, ...
7, 3, 7, -2, 15, -5, 9, ...
...
MATHEMATICA
Table[Function[n, If[k + n == 0, 0, DivisorSigma[1, k + n]] - If[k == 0, 0, DivisorSigma[1, k]] - n][m - k], {m, 12}, {k, m, 1, -1}] // Flatten (* Michael De Vlieger, Jul 20 2017 *)
PROG
(PARI) T(n, k) = sigma(k + n) - sigma(k) - n;
(PARI) a(n) = n++; my(s = ceil((-1+sqrt(1+8*n))/2)); r=n-binomial(s, 2)-1; k=s-r; T(r, k) \\ David A. Corneth, Jul 20 2017
(Python)
from sympy import divisor_sigma
l=[]
def T(n, k):
return 0 if n==0 or k==0 else divisor_sigma(k + n) - divisor_sigma(k) - n
for n in range(11): l+=[T(k, n - k + 1) for k in range(n + 1)]
print(l) # Indranil Ghosh, Jul 21 2017
CROSSREFS
Cf. A000203 (sigma), A015886.
Sequence in context: A231728 A303545 A306191 * A307356 A091426 A053761
KEYWORD
sign,tabl
AUTHOR
Michel Marcus, Jul 20 2017
STATUS
approved

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Last modified May 28 15:12 EDT 2024. Contains 372916 sequences. (Running on oeis4.)