OFFSET
1,2
REFERENCES
Michael Baake, "Solution of the coincidence problem in dimensions d <= 4", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from G. C. Greubel)
M. Baake and N. Neumarker, A Note on the Relation Between Fixed Point and Orbit Count Sequences, JIS 12 (2009) 09.4.4, Section 3.
FORMULA
f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=5.
Multiplicative with a(p^e) = Product_{k=1..4} (p^(e+k)-1)/(p^k-1).
Dirichlet g.f.: zeta(s)*zeta(s-1)*zeta(s-2)*zeta(s-3)*zeta(s-4). Dirichlet convolution of A038991 with A000583. - R. J. Mathar, Mar 31 2011
Sum_{k=1..n} a(k) ~ c * n^5, where c = Pi^6*zeta(3)*zeta(5)/2700 = 0.443822... . - Amiram Eldar, Oct 19 2022
MATHEMATICA
a[n_] := DivisorSum[n, #*DivisorSum[#, #*DivisorSum[#, #*DivisorSum[#, # &] &] &] &]; Array[a, 50] (* Jean-François Alcover, Dec 02 2015, after Joerg Arndt *)
f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 4}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)
PROG
(PARI) a(n)=sumdiv(n, x, x * sumdiv(x, y, y * sumdiv(y, z, z * sumdiv(z, w, w ) ) ) ); /* Joerg Arndt, Oct 07 2012 */
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
EXTENSIONS
Offset changed from 0 to 1 by R. J. Mathar, Mar 31 2011
More terms from Joerg Arndt, Oct 07 2012
STATUS
approved