|
Search: id:A121443
|
|
|
| A121443 |
|
Sum of divisors d of n which are odd and n/d is not divisible by 3. |
|
+0
3
|
|
| 1, 1, 3, 1, 6, 3, 8, 1, 9, 6, 12, 3, 14, 8, 18, 1, 18, 9, 20, 6, 24, 12, 24, 3, 31, 14, 27, 8, 30, 18, 32, 1, 36, 18, 48, 9, 38, 20, 42, 6, 42, 24, 44, 12, 54, 24, 48, 3, 57, 31, 54, 14, 54, 27, 72, 8, 60, 30, 60, 18, 62, 32, 72, 1, 84, 36, 68, 18, 72, 48, 72, 9, 74, 38, 93, 20, 96, 42
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
REFERENCES
|
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 86, Eq. (33.124).
|
|
FORMULA
|
Expansion of c(q)c(q^2)/9 where c(q) is the third function in a cubic AGM analogue described by Borwein.
Euler transform of period 6 sequence [ 1, 2, -2, 2, 1, -4, ...].
Expansion of (eta(q^3)eta(q^6))^3/(eta(q)eta(q^2)) in powers of q.
Multiplicative with a(2^e)=1, a(3^e)=3^e, a(p^e)=(p^(e+1)-1)/(p-1) if p>3.
a(2n)=a(n), a(3n)=3a(n).
G.f.: x Product_{k>0} ((1-x^(3k))(1-x^(6k)))^3/((1-x^k)(1-x^(2k))) = Sum_{k>0} k*x^k*(1-x^k)/(1+x^(3*k)).
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)= v^4 -u*w* (u-2*v)* (v-2*w).
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)= +u1^3*u6 +2*u2^3*u3 +3*u2^2*u3^2 +6*u1*u2*u3*u6 +48*u2^2*u6^2 -3*u1^2*u2*u6 -3*u1*u2*u3^2 -24*u2^2*u3*u6 -30*u1*u2*u6^2 . - Michael Somos Apr 18 2007
|
|
PROGRAM
|
(PARI) {a(n)=if(n<1, 0, sumdiv(n, d, (d%2)*(n/d%3>0)*d))}
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x^3+A)*eta(x^6+A))^3/(eta(x+A)*eta(x^2+A)), n))}
|
|
CROSSREFS
|
a(6n+5)=6*A098098(n).
Sequence in context: A039805 A094504 A107884 this_sequence A008795 A132180 A126191
Adjacent sequences: A121440 A121441 A121442 this_sequence A121444 A121445 A121446
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
Michael Somos, Jul 30 2006, Apr 18 2007
|
|
|
Search completed in 0.002 seconds
|
