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A033273 Number of nonprime divisors of n. 20
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 4, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 3, 4, 1, 5, 1, 5, 2, 2, 2, 7, 1, 2, 2, 6, 1, 5, 1, 4, 4, 2, 1, 8, 2, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 9, 1, 2, 4, 6, 2, 5, 1, 4, 2, 5, 1, 10, 1, 2, 4, 4, 2, 5, 1, 8, 4, 2, 1, 9, 2, 2, 2, 6, 1, 9, 2, 4, 2, 2, 2, 10, 1, 4, 4, 7, 1, 5, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(A055079(n)) = n and a(m) <> n for m < A055079(n). - Reinhard Zumkeller, Dec 16 2013

LINKS

Ray Chandler, Table of n, a(n) for n=1..100000

FORMULA

a(n) = A000005(n) - A001221(n).

G.f.: Sum_{k>=1} (x^k - x^prime(k))/((1 - x^k)*(1 - x^prime(k))). - Ilya Gutkovskiy, Jan 17 2017

Dirichlet g.f.: zeta(s)*(zeta(s)-primezeta(s)). - Benedict W. J. Irwin, Jul 11 2018

MATHEMATICA

Table[Length[Select[Divisors[n], ! PrimeQ[#] &]], {n, 104}] (* Jayanta Basu, May 23 2013 *)

Table[DivisorSigma[0, n] - PrimeNu[n], {n, 100}] (* Vincenzo Librandi, May 17 2017 *)

PROG

(Haskell)

a033273 = length . filter ((== 0) . a010051) . a027750_row

-- Reinhard Zumkeller, Dec 16 2013

(PARI) a(n) = numdiv(n) - omega(n); \\ Michel Marcus, Apr 28 2016

(MAGMA) [NumberOfDivisors(n) - #PrimeDivisors(n): n in [1..150]]; // Vincenzo Librandi, May 17 2017

CROSSREFS

Cf. A000005, A001221.

Cf. A059992, A180040.

Cf. A010051, A027750.

Sequence in context: A294894 A076526 A226378 * A319685 A034836 A316365

Adjacent sequences:  A033270 A033271 A033272 * A033274 A033275 A033276

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Reinhard Zumkeller, Sep 02 2003

Corrected error in offset. - Jaroslav Krizek, May 04 2009

Extended by Ray Chandler, Aug 07 2010

STATUS

approved

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Last modified April 23 03:26 EDT 2019. Contains 322380 sequences. (Running on oeis4.)