A081707 a(n) = tau(n) - bigomega(n) = A000005(n) - A001222(n).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 5, 1, 1, 2, 2, 2, 5, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 8, 1, 2, 3, 1, 2, 5, 1, 3, 2, 5, 1, 7, 1, 2, 3, 3, 2, 5, 1, 5, 1, 2, 1, 8, 2, 2, 2, 4, 1, 8, 2, 3, 2, 2, 2, 6, 1, 3, 3, 5, 1, 5, 1, 4, 5

Offset: 1

Author

Vladeta Jovovic, Apr 03 2003

Keywords

• nonn

Comments

Number of divisors of n that are not positive powers of primes (cf. A000961). - Benoit Cloitre, May 03 2003; corrected Dec 16 2008 at the suggestion of Ray Chandler.

a(n) = 1 iff n is in A000961. - Robert Israel, Nov 23 2015

a(n) = 2 iff n is in A006881. - Altug Alkan, Nov 23 2015

a(n) = 3 iff n is in A054753. - Michel Marcus, Nov 24 2015

Examples

			After first statement in comment section, a(60) = 8 because we have: 1,6,10,12,15,20,30,60. The divisors 2,3,4,5 are excluded from the count. - _Geoffrey Critzer_, Nov 22 2015
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033273(n) = tau(n) - omega(n) = A000005(n) - A001221(n).

Cf. A000961.

Programs

Maple

seq(numtheory:-tau(n)-numtheory:-bigomega(n), n=1..300); # Robert Israel, Nov 23 2015

Mathematica

Table[DivisorSigma[0, n] - PrimeOmega[n], {n, 1, 105}] (* Geoffrey Critzer, Nov 22 2015 *)

PARI

first(m)=vector(m,n,numdiv(n) - bigomega(n)) \\ Anders Hellström, Nov 22 2015