The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A116607 Sum of the divisors of n which are not divisible by 9. 11
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 475 Entry 7(i). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 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) = 4 if e>0, a(p^e) = (p^(e+1) - 1) / (p - 1) otherwise. G.f.: Sum_{k>0} k * x^k /(1 - x^k) - 9*k * x^(9*k) / (1 - x^(9*k)). L.g.f.: log(Product_{k>=1} (1 - x^(9*k))/(1 - x^k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 14 2018 EXAMPLE q + 3*q^2 + 4*q^3 + 7*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + 15*q^8 + 4*q^9 + ... MATHEMATICA With[{c=9Range[20]}, Table[Total[Complement[Divisors[i], c]], {i, 80}]] [From Harvey P. Dale, Dec. 19, 2010] Drop[CoefficientList[Series[Sum[k * x^k /(1 - x^k) - 9*k * x^(9*k) / (1 - x^(9*k)) , {k, 1, 100}], {x, 0, 100}], x], 1] (* Indranil Ghosh, Mar 25 2017 *) f[p_, e_] := If[p == 3, 4, (p^(e + 1) - 1)/(p - 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 17 2020 *) PROG (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)} (PARI) q='q+O('q^66); Vec( (eta(q^3)^10/(eta(q)*eta(q^9))^3 - 1) /3 ) \\ Joerg Arndt, Mar 25 2017 (Python) from sympy import divisors print([sum(i for i in divisors(n) if i%9) for n in range(1, 101)]) # Indranil Ghosh, Mar 25 2017 CROSSREFS A096726(n) = 3*a(n) if n>0. Cf. A046897, A046913, A113957, A116073, A284326, A284341. Sequence in context: A333926 A051378 A254981 * A107749 A093811 A088000 Adjacent sequences:  A116604 A116605 A116606 * A116608 A116609 A116610 KEYWORD nonn,mult AUTHOR Michael Somos, Feb 19 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 10 01:03 EDT 2021. Contains 343747 sequences. (Running on oeis4.)