|
| |
|
|
A062369
|
|
Dirichlet convolution of n and tau^2(n).
|
|
4
| |
|
|
1, 6, 7, 21, 9, 42, 11, 58, 30, 54, 15, 147, 17, 66, 63, 141, 21, 180, 23, 189, 77, 90, 27, 406, 54, 102, 106, 231, 33, 378, 35, 318, 105, 126, 99, 630, 41, 138, 119, 522, 45, 462, 47, 315, 270, 162, 51, 987, 86, 324, 147, 357, 57, 636, 135, 638, 161, 198, 63, 1323
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Dirichlet convolution of A000027 and A035116.
Inverse Mobius transform of A060724. - R. J. Mathar, Oct 15 2011
|
|
|
FORMULA
| a(n) = Sum_{i|n,j|n} sigma(i)*sigma(j)/sigma(LCM(i,j)), where sigma(n) = sum of divisors of n.
a(n) = Sum_{i|d, j|d} sigma(gcd(i, j)) = Sum_{d|n} d*tau(n/d)^2, where tau(n) = number of divisors of n. Multiplicative with a(p^e) = (1-p^(3+e)-p^(2+e)+e^2+4*p^2+p^2*e^2+2*e-3*p+4*p^2*e-6*e*p-2*e^2*p)/(1-p)^3.
Dirichlet g.f. (zeta(s))^4*zeta(s-1)/zeta(2*s). - R. J. Mathar, Feb 09 2011
|
|
|
CROSSREFS
| Cf. A000203, A060648.
Cf. A000005, A060724, A064950, A062369, A062368, A062380.
Sequence in context: A041076 A041771 A042757 * A048062 A081284 A185509
Adjacent sequences: A062366 A062367 A062368 * A062370 A062371 A062372
|
|
|
KEYWORD
| nonn,mult
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 07 2001
|
| |
|
|
