|
| |
| |
|
|
|
0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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... .
|
|
|
REFERENCES
|
József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter V, page 164.
|
|
|
LINKS
|
|
|
|
FORMULA
|
Sum_{k=1..n} a(k) = c * n + O(sqrt(n) * log(n)^3/log(log(n))), where c = Sum_{k>=1} d(k) * A001222(k) is a constant, d(k) is the asymptotic density of the set {m | A000688(m) = k} (e.g., d(1) = A059956, d(2) = A271971, d(3) appears in A048109) (Ivić, 1983).
|
|
|
MATHEMATICA
|
Table[PrimeOmega[FiniteAbelianGroupCount[n]], {n, 1, 100}]
|
|
|
PROG
|
(PARI) a(n) = bigomega(vecprod(apply(numbpart, factor(n)[, 2])));
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
