|
Search: id:A116607
|
|
|
| A116607 |
|
Sum of the divisors of n which are not divisble by 9. |
|
+0
1
|
|
| 1, 3, 4, 7, 6, 12, 8, 15, 4, 18, 12, 28, 14, 24, 24, 31, 18, 12, 20, 42, 32, 36, 24, 60, 31, 42, 4, 56, 30, 72, 32, 63, 48, 54, 48, 28, 38, 60, 56, 90, 42, 96, 44, 84, 24, 72, 48, 124, 57, 93, 72, 98, 54, 12, 72, 120, 80, 90, 60, 168, 62, 96, 32, 127, 84, 144, 68, 126, 96
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 475 Entry 7(i).
J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi's identity and the AGM, Trans. Amer. Math. Soc., 323 (1991), no. 2, 691-701. MR1010408 (91e:33012)
|
|
FORMULA
|
Expansion of (eta(q^3)^10/(eta(q)eta(q^9))^3-1)/3 in powers of q.
a(n) is multiplicative with a(3^e) = 1+3*(e>0), a(p^e) = (p^(e+1)-1)/(p-1) otherwise.
G.f. Sum_{k>0} k*x^k/(1-x^k) -9k*x^(9k)/(1-x^(9k)).
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 0, sigma(n)-if(n%9==0, 9*sigma(n/9)))
(PARI) a(n)=polcoeff(sum(k=1, n, k*(x^k/(1-x^k)-9*x^(9*k)/(1-x^(9*k))), x*O(x^n)), n)
|
|
CROSSREFS
|
A097626(n)=3*a(n) if n>0.
Sequence in context: A073183 A049418 A051378 this_sequence A107749 A093811 A088000
Adjacent sequences: A116604 A116605 A116606 this_sequence A116608 A116609 A116610
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
Michael Somos, Feb 19 2006
|
|
|
Search completed in 0.002 seconds
|
