OFFSET
1,36
COMMENTS
First differs from A364388 at n = 42.
The sums of the first 10^k terms, for k = 1, 2, ..., are 10, 102, 1024, 10285, 102988, 1030280, 10304021, 103043644, 1030448091, 10304515936, ... . From these values the asymptotic mean of this sequence, whose existence was proven by Ivić (1983) (see the Formula section), can be empirically evaluated by 1.0304... .
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter XIII, page 477-478.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős and Aleksandar Ivić, On the iterates of the enumerating function of finite Abelian groups, Bull. Cl. Sci. Math. Nat., Sci. Math., Vol. 17 (1989), pp. 13-22; alternative link.
Aleksandar Ivić, On the number of abelian groups of a given order and on certain related multiplicative functions, Journal of Number Theory, Vol. 16, No. 1 (1983), pp. 119-137. See p. 131, eq. 4.2.
FORMULA
MATHEMATICA
Table[FiniteAbelianGroupCount[FiniteAbelianGroupCount[n]], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 15 2024
STATUS
approved