|
| |
|
|
A127527
|
|
Triangle T(n,k)= tau(k)*phi(n/k) if k|n, else T(n,k)=0.
|
|
2
| |
|
|
1, 1, 2, 2, 0, 2, 2, 2, 0, 3, 4, 0, 0, 0, 2, 2, 4, 2, 0, 0, 4, 6, 0, 0, 0, 0, 0, 2, 4, 4, 0, 3, 0, 0, 0, 4, 6, 0, 4, 0, 0, 0, 0, 0, 3, 4, 8, 0, 0, 2, 0, 0, 0, 0, 4
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Tau is the number of divisors A000005, and phi the Euler totient A000010.
|
|
|
FORMULA
| T(n,k) = A000005(k)*A054523(n,k).
T(n,1) = A000010(n).
T(n,n) = A000005(n).
Sum_{k=1..n} T(n,k) = A000203(n).
|
|
|
EXAMPLE
| First few rows of the triangle are:
1;
1, 2;
2, 0, 2;
2, 2, 0, 3;
4, 0, 0, 0, 2;
2, 4, 2, 0, 0, 4;
6, 0, 0, 0, 0, 0, 2;
4, 4, 0, 3, 0, 0, 0, 4;
...
|
|
|
MAPLE
| A127527 := proc(n, k) if n mod k = 0 then numtheory[tau](k)*numtheory[phi](n/k) ; else 0; end if; end proc: # R. J. Mathar, Apr 11 2011
|
|
|
CROSSREFS
| Cf. A054523, A000005, A000010, A000203.
Sequence in context: A029321 A029310 A134131 * A177225 A153239 A141661
Adjacent sequences: A127524 A127525 A127526 * A127528 A127529 A127530
|
|
|
KEYWORD
| nonn,tabl,easy
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 17 2007
|
|
|
EXTENSIONS
| Definition clarified by R. J. Mathar, Apr 11 2011
|
| |
|
|
