OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..3329 (terms 1..500 from T. D. Noe)
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
FORMULA
L.g.f.: A(x) = Sum_{n>=1} log( G(x^n,n) ) where G(x,n) = 1 + x*G(x,n)^n. L.g.f. A(x) satisfies: exp(A(x)) = g.f. of A110448. - Paul D. Hanna, Nov 10 2007
a(n) = Sum_{k=1..n} binomial(n,gcd(n,k))/phi(n/gcd(n,k)) = Sum_{k=1..n} binomial(n,n/gcd(n,k))/phi(n/gcd(n,k)) where phi = A000010. - Richard L. Ollerton, Nov 08 2021
a(n) = n+1 iff n is prime. - Bernard Schott, Nov 30 2021
EXAMPLE
MATHEMATICA
f[n_] := Sum[ Binomial[n, d], {d, Divisors@ n}]; Array[f, 37] (* Robert G. Wilson v, Apr 23 2005 *)
Total[Binomial[#, Divisors[#]]]&/@Range[40] (* Harvey P. Dale, Dec 08 2018 *)
PROG
(PARI) {a(n)=n*polcoeff(sum(m=1, n, log(1/x*serreverse(x/(1+x^m +x*O(x^n))))), n)} /* Paul D. Hanna, Nov 10 2007 */
(PARI) {a(n)=sumdiv(n, d, binomial(n, d))} /* Paul D. Hanna, Nov 10 2007 */
(Haskell)
a056045 n = sum $ map (a007318 n) $ a027750_row n
-- Reinhard Zumkeller, Aug 13 2013
(Python)
from math import comb
from sympy import divisors
def A056045(n): return sum(comb(n, d) for d in divisors(n, generator=True)) # Chai Wah Wu, Jul 22 2024
KEYWORD
nice,nonn
AUTHOR
Labos Elemer, Jul 25 2000
STATUS
approved