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A305054
If n = Product_i prime(x_i)^k_i, then a(n) = Sum_i k_i * omega(x_i), where omega = A001221 is number of distinct prime factors.
3
0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 2, 2, 1, 0, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 1, 3, 1, 2, 1, 2, 2, 2, 2, 1, 3, 2, 1, 2, 2, 1, 2, 2, 1, 3, 0, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 2, 1, 4, 1, 1, 2, 2, 2, 3
OFFSET
1,9
FORMULA
Totally additive with a(prime(n)) = omega(n).
a(n) = A305053(n) + A001221(n). - Michel Marcus, Jun 09 2018
MATHEMATICA
Table[If[n==1, 0, Total@Cases[FactorInteger[n], {p_, k_}:>k*PrimeNu[PrimePi[p]]]], {n, 100}]
PROG
(PARI) a(n) = {my(f=factor(n)); sum(k=1, #f~, f[k, 2]*omega(primepi(f[k, 1]))); } \\ Michel Marcus, Jun 09 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 24 2018
STATUS
approved