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.

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

Links

Table of n, a(n) for n=1..87.

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

Crossrefs

Cf. A001221, A003963, A056239, A076078, A112798, A286520, A290103, A302242, A304714, A304716, A305052, A305053.

Sequence in context: A351089 A133831 A325613 * A238097 A066955 A089048

Adjacent sequences: A305051 A305052 A305053 * A305055 A305056 A305057

Keyword

nonn

Author

Gus Wiseman, May 24 2018

Status

approved