|
|
A278908
|
|
Multiplicative with a(p^e) = 2^omega(e), where omega = A001221.
|
|
14
|
|
|
1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
The number of exponential unitary (or e-unitary) divisors of n and the number of exponential squarefree exponential divisors (or e-squarefree e-divisors) of n. These are divisors of n = Product p(i)^a(i) of the form Product p(i)^b(i) where each b(i) is a unitary divisor of a(i) in the first case, or each b(i) is a squarefree divisor of a(i) in the second case. - Amiram Eldar, Dec 29 2018
|
|
LINKS
|
|
|
FORMULA
|
Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = Product_{p prime} (1 + Sum_{k>=2} (2*omega(k) - 2^omega(k-1))/p^k) = 1.5431653193... (Tóth, 2007). - Amiram Eldar, Nov 08 2020
|
|
MAPLE
|
local a, p, e;
a := 1;
if n =1 then
;
else
for p in ifactors(n)[2] do
e := op(2, p) ;
end do:
end if;
a ;
end proc:
|
|
MATHEMATICA
|
Table[Times @@ Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 1 :> 2^PrimeNu[e]], {n, 105}] (* Michael De Vlieger, Jul 29 2017 *)
|
|
PROG
|
(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = 2^omega(f[k, 2]); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Jul 28 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|