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

1,25

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.

Links

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

Formula

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

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

Example

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

Mathematica

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

Prog

(Haskell)
a106799 = a001222 . a065330  -- Reinhard Zumkeller, Nov 19 2015
(PARI) a(n) = bigomega(n) - valuation(n, 2) - valuation(n, 3); \\ Michel Marcus, Jan 16 2022

Crossrefs

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

Sequence in context: A291954 A375670 A339885 * A212210 A127499 A198068

Adjacent sequences: A106796 A106797 A106798 * A106800 A106801 A106802

Keyword

nonn

Author

Henry Bottomley, May 17 2005

Status

approved