OFFSET
1,36
COMMENTS
First differs from A369164 at n = 36.
The sums of the first 10^k terms, for k = 1, 2, ..., are 3, 42, 450, 4592, 46185, 462402, 4625478, 46258861, 462599818, 4626029362, ... . 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 0.4626... .
First differs from A056170 at n=128, 256, 384, 512, 640.... - R. J. Mathar, Jan 18 2024
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter V, page 164.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
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. 4.5.
FORMULA
MATHEMATICA
Table[PrimeOmega[FiniteAbelianGroupCount[n]], {n, 1, 100}]
PROG
(PARI) a(n) = bigomega(vecprod(apply(numbpart, factor(n)[, 2])));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 15 2024
STATUS
approved