A033273 Number of nonprime divisors of n.
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
Offset: 1
Keywords
Links
- Ray Chandler, Table of n, a(n) for n=1..100000
Crossrefs
Programs
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Haskell
a033273 = length . filter ((== 0) . a010051) . a027750_row -- Reinhard Zumkeller, Dec 16 2013
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Magma
[NumberOfDivisors(n) - #PrimeDivisors(n): n in [1..150]]; // Vincenzo Librandi, May 17 2017
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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 *) Table[Count[Divisors[n],?CompositeQ],{n,110}]+1 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Jun 11 2019 *) -
PARI
a(n) = numdiv(n) - omega(n); \\ Michel Marcus, Apr 28 2016
Formula
a((n)) = n and a(m) <> n for m < A055079(n). - Reinhard Zumkeller, Dec 16 2013
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
Sum_{k=1..n} a(k) ~ n*log(n) - n*log(log(n)) + (2*gamma - 1 - B)*n, where gamma is Euler's constant (A001620) and B is Mertens's constant (A077761). - Amiram Eldar, Nov 27 2022
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