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A127173
T(n,k) = A007427(n/k) if k divides n, T(n,k) = 0 otherwise.
1
1, -2, 1, -2, 0, 1, 1, -2, 0, 1, -2, 0, 0, 0, 1, 4, -2, -2, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, 1, 1, 0, -2, 0, 0, 0, 0, 0, 1, 4, -2, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 4, 1, -2, 0, -2, 0, 0, 0, 0, 0, 1
OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
FORMULA
Square of A054525 as lower triangular matrix.
A007431(n) = Sum_{k=1, n} k*T(n,k).
A007428(n) = Sum_{k=1..n} mu(k)*T(n,k).
EXAMPLE
First few rows of the triangle:
1;
-2, 1;
-2, 0, 1;
1, -2, 0, 1;
-2, 0, 0, 0, 1;
4, -2, -2, 0, 0, 1;
-2, 0, 0, 0, 0, 0, 1;
0, 1, 0, -2, 0, 0, 0, 1;
1, 0, -2, 0, 0, 0, 0, 0, 1;
4, -2, 0, 0, -2, 0, 0, 0, 0, 1;
...
PROG
(PARI) \\ here b(n) is A007427(n).
b(n)={sumdiv(n, d, moebius(d) * moebius(n/d))}
T(n, k)={if(n%k==0, b(n/k), 0)} \\ Andrew Howroyd, Feb 20 2022
CROSSREFS
Row sums are A008683.
Column 1 is A007427.
Sequence in context: A303975 A171099 A337253 * A362867 A035160 A353328
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Jan 06 2007
EXTENSIONS
Missing a(10)-a(14) and a(56) and beyond from Andrew Howroyd, Feb 20 2022
STATUS
approved