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A080256 Sum of numbers of distinct and of all prime factors of n. 7
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; text; internal format)
OFFSET

1,2

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.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = Omega(n) + omega(n) = A001221(n) + A001222(n).

Additive with a(p^e) = e + 1.

MATHEMATICA

f[n_] := Plus @@ (Last /@ FactorInteger[n] + 1); Table[ f[n], {n, 105}] (* Robert G. Wilson v, Aug 03 2005 *)

CROSSREFS

Cf. A046660.

Sequence in context: A084302 A289872 A301855 * A289849 A299701 A286605

Adjacent sequences:  A080253 A080254 A080255 * A080257 A080258 A080259

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 10 2003

STATUS

approved

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Last modified February 22 20:16 EST 2019. Contains 320404 sequences. (Running on oeis4.)