A091371 Smallest prime factor of n - number of prime factors of n with multiplicity.

1, 1, 2, 0, 4, 0, 6, -1, 1, 0, 10, -1, 12, 0, 1, -2, 16, -1, 18, -1, 1, 0, 22, -2, 3, 0, 0, -1, 28, -1, 30, -3, 1, 0, 3, -2, 36, 0, 1, -2, 40, -1, 42, -1, 0, 0, 46, -3, 5, -1, 1, -1, 52, -2, 3, -2, 1, 0, 58, -2, 60, 0, 0, -4, 3, -1, 66, -1, 1, -1, 70, -3, 72, 0, 0, -1, 5, -1, 78, -3

Offset: 1

Author

Reinhard Zumkeller, Jan 04 2004

Keywords

• sign

Comments

a(n) = A020639(n) - A001222(n).

a(A091375(n)) < 0. a(A091376(n)) = 0. a(A091377(n)) > 0.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020639 (lpf), A001222 (Omega).

Cf. A091372, A091373, A091374, A091375, A091376, A091377.

Programs

Maple

with(numtheory); A091371:=n->`if`(n=1,1,min(op(factorset(n)))-bigomega(n)); seq(A091371(k), k=1..100); # Wesley Ivan Hurt, Oct 27 2013

Mathematica

Array[FactorInteger[#][[1,1]]-PrimeOmega[#]&,80] (* Harvey P. Dale, May 25 2012 *)

Extensions

Definition clarified by Harvey P. Dale, May 25 2012