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A080256
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Sum of numbers of distinct and of all prime factors of n.
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5
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0, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 5, 2, 4, 4, 5, 2, 5, 2, 5, 4, 4, 2, 6, 3, 4, 4, 5, 2, 6, 2, 6, 4, 4, 4, 6, 2, 4, 4, 6, 2, 6, 2, 5, 5, 4, 2, 7, 3, 5, 4, 5, 2, 6, 4, 6, 4, 4, 2, 7, 2, 4, 5, 7, 4, 6, 2, 5, 4, 6, 2, 7, 2, 4, 5, 5, 4, 6, 2, 7, 5, 4, 2, 7, 4, 4, 4, 6, 2, 7, 4, 5, 4, 4, 4, 8, 2, 5, 5, 6, 2, 6, 2, 6, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = 2 iff n is prime, A000040; a(n) > 2 iff n is composite, A002808; a(n) <= 3 iff n is prime or square of prime, A000430; a(n) = 3 iff n is square of prime, A001248; a(A080257(n)) > 3;
a(n) <= 4 iff product of proper divisors <= n^2, A007964; a(n) = 4 iff n has four divisors, A030513; a(n) > 4 iff product of proper divisors > n^2, A058080; a(A064598(n)) <= 5; a(A080258(n)) = 5.
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FORMULA
| a(n) = Omega(n) + omega(n) = A001221(n) + A001222(n).
Additive with a(p^e) = e + 1.
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MATHEMATICA
| f[n_] := Plus @@ (Last /@ FactorInteger[n] + 1); Table[ f[n], {n, 105}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 03 2005)
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CROSSREFS
| Cf. A046660.
Sequence in context: A138707 A095048 A084302 * A035149 A074848 A167447
Adjacent sequences: A080253 A080254 A080255 * A080257 A080258 A080259
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 10 2003
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