|
| |
|
|
A366073
|
|
The number of composite "Fermi-Dirac primes" (A082522) dividing n.
|
|
2
|
|
|
|
0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,16
|
|
|
COMMENTS
|
First differs from A071325 at n = 36.
The number of "Fermi-Dirac primes" that are infinitary divisors of n is A064547(n).
|
|
|
LINKS
|
|
|
|
FORMULA
|
Additive with a(p^e) = floor(log_2(e)) = A000523(e).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} P(2^k) = 0.53331724743088069672..., where P(s) is the prime zeta function.
|
|
|
MATHEMATICA
|
f[p_, e_] := Floor[Log2[e]]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
|
|
|
PROG
|
(PARI) a(n) = vecsum(apply(exponent, factor(n)[, 2]));
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
