OFFSET
1,4
COMMENTS
The sums of the first 10^k terms, for k = 1, 2, ..., are 13, 143, 1486, 15054, 151067, 1511982, 15123465, 151245456, 1512484372, 15124927227, ... . 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 1.512... .
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter II, page 73.
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. 4.3.
FORMULA
MATHEMATICA
Table[DivisorSigma[0, FiniteAbelianGroupCount[n]], {n, 1, 100}]
PROG
(PARI) a(n) = numdiv(vecprod(apply(numbpart, factor(n)[, 2])));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 15 2024
STATUS
approved