A106799 Number of prime factors of n apart from 2 or 3, counted with multiplicity.

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

Offset: 1

Author

Henry Bottomley, May 17 2005

Keywords

• nonn

Comments

Self-similar in every second and in every third term, i.e., a(n) = a(2n) = a(3n).

Logarithmic since a(b*c) = a(b) + a(c).

Coincidentally, a(n) = A101040(n+78) for 1 < n < 20.

Examples

			a(24) = 0 since 24 = 2*2*2*3.
a(25) = 2 since 25 = 5*5.
a(26) = 1 since 26 = 2*13.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A007814, A007949, A027746, A065330, A087436, A101040, A169611.

Programs

Haskell

a106799 = a001222 . a065330  -- Reinhard Zumkeller, Nov 19 2015

Mathematica

a[n_] := PrimeOmega[n] - IntegerExponent[n, 2] - IntegerExponent[n, 3]; Array[a, 100] (* Amiram Eldar, Jan 16 2022 *)

PARI

a(n) = bigomega(n) - valuation(n, 2) - valuation(n, 3); \\ Michel Marcus, Jan 16 2022

Formula

a(n) = A001222(n) - A007814(n) - A007949(n) = A087436(n) - A007949(n).

a(n) = A001222(A065330(n)). - Reinhard Zumkeller, May 19 2005