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A005087 Number of distinct odd primes dividing n. 12
0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 0, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,15

COMMENTS

a(n) = A001221(n) - 1 + n mod 2. - Reinhard Zumkeller, Sep 03 2003

LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000

FORMULA

Additive with a(p^e) = 0 if p = 2, 1 otherwise.

O.g.f. Sum_{p=odd prime} x^p/(1-x^p). - Geoffrey Critzer, Nov 06 2012

MATHEMATICA

nn=100; a=Sum[x^p/(1-x^p), {p, Table[Prime[n], {n, 2, nn}]}]; Drop[CoefficientList[Series[a, {x, 0, nn}], x], 1] (* Geoffrey Critzer, Nov 06 2012 *)

Array[PrimeNu[#] - Boole[EvenQ[#]] &, 102] (* Lei Zhou, Dec 03 2012 *)

PROG

(Sage)

def A005087(n) : return len(filter(is_prime, divisors(n))) + n % 2 - 1

[A005087(n) for n in (1..80)]  # Peter Luschny, Feb 01 2012

(Haskell)

a005087 n = a001221 n + n `mod` 2 - 1 -- Reinhard Zumkeller, Feb 28 2014

CROSSREFS

Cf. A087436.

Sequence in context: A282355 A199322 A284203 * A050332 A216658 A214020

Adjacent sequences:  A005084 A005085 A005086 * A005088 A005089 A005090

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Reinhard Zumkeller, Sep 03 2003

STATUS

approved

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Last modified August 25 03:10 EDT 2019. Contains 326318 sequences. (Running on oeis4.)