A087624 a(n)=0 if n is prime, A001221(n) otherwise.

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 1, 2, 0, 3, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 3, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 3, 0, 2, 2, 1, 2, 3, 0, 2, 2, 3, 0, 2, 0, 2, 2, 2, 2, 3, 0, 2, 1, 2, 0, 3, 2, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 3, 0, 2, 3

Offset: 1

Author

Michele Dondi (bik.mido(AT)tiscalinet.it), Sep 14 2003

Keywords

• nonn
• easy

Comments

Number of prime divisors of n, but excluding n itself if n is prime.

Number of non-associated primes in the ring Z_n.

Also for n > 1 the number of times n is crossed off in the sieve of Eratosthenes (A000040). - Reinhard Zumkeller, Oct 17 2008

Number of primes that are proper divisors of n. - Omar E. Pol, Dec 27 2008

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000
• Index entries for sequences generated by sieves [From _Reinhard Zumkeller_, Oct 17 2008]

Crossrefs

Cf. A001221, A010051, A087625.

A144489 gives partial sums.

Programs

Haskell

a087624 n = if a010051 n == 1 then 0 else a001221 n
-- Reinhard Zumkeller, Apr 05 2013

Maple

with(numtheory); f:=proc(n) if isprime(n) then nops(factorset(n))-1 else nops(factorset(n)) fi; end;

Mathematica

Array[If[PrimeQ[#],0,PrimeNu[#]]&,110] (* Harvey P. Dale, Mar 27 2013 *)

PARI

a(n) = if (isprime(n), 0, omega(n)); \\ Michel Marcus, Nov 06 2022

Formula

a(n) = A001221(n) * A005171(n). - Jason Kimberley, Nov 19 2014

G.f.: Sum_{k>=1} x^(2*prime(k)) / (1 - x^prime(k)). - Ilya Gutkovskiy, Apr 13 2021

a(n) = omega(n) - c(n), where c = A010051. - Wesley Ivan Hurt, Jun 23 2024

Extensions

Edited by N. J. A. Sloane, Dec 11 2008