|
|
A305053
|
|
If n = Product_i prime(x_i)^k_i, then a(n) = Sum_i k_i * omega(x_i) - omega(n), where omega = A001221 is number of distinct prime factors.
|
|
2
|
|
|
0, -1, 0, -1, 0, -1, 0, -1, 1, -1, 0, -1, 1, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 1, 0, 2, -1, 1, -1, 0, -1, 0, -1, 0, 0, 1, -1, 1, -1, 0, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 0, -1, 0, -1, 1, 0, 1, 0, 1, -1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,27
|
|
LINKS
|
|
|
FORMULA
|
Totally additive with a(prime(n)) = omega(n) - 1.
|
|
EXAMPLE
|
2925 = prime(2)^2 * prime(3)^2 * prime(6)^1, so a(2925) = 2*1 + 2*1 + 1*2 - 3 = 3.
|
|
MATHEMATICA
|
Table[If[n==1, 0, Total@Cases[FactorInteger[n], {p_, k_}:>(k*PrimeNu[PrimePi[p]]-1)]], {n, 100}]
|
|
PROG
|
(PARI) a(n) = {my(f=factor(n)); sum(k=1, #f~, f[k, 2]*omega(primepi(f[k, 1]))) - omega(n); } \\ Michel Marcus, Jun 09 2018
|
|
CROSSREFS
|
Cf. A001221, A003963, A056239, A112798, A286520, A290103, A302242, A304714, A304716, A305052, A305054.
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|