A116452 Number of prime factors of A116451(n).

1, 1, 2, 2, 1, 1, 2, 2, 1, 3, 1, 3, 2, 2, 1, 2, 2, 3, 3, 1, 3, 1, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 5, 4, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 1, 3, 3, 4, 1, 3, 1, 4, 3, 2, 1, 5, 1, 3, 2, 5, 1, 3, 2, 3, 3, 2

Offset

0,3

Links

Table of n, a(n) for n=0..104.

Formula

a(n) = A001222(A116451(n)).

Record values: A116453(n) = a(A116454(n)).

Prog

(Python)
from sympy import primeomega
def A116452(n): return (1, 1, 2, 2, 1, 1, 2, 2, 1, 3, 1, 3, 2, 2, 1, 2, 2, 3, 3, 1, 3, 1, 2)[n] if n<23 else primeomega(n+1+(m:=(n+1).bit_length()+((n+1)//3).bit_length())+(n+1+m>=(1<<(m+1>>1) if m&1 else 3<<(m+1>>1)-1))) # Chai Wah Wu, Jan 25 2026

Crossrefs

Cf. A001222, A116451, A116453, A116454.

Sequence in context: A271381 A393576 A086247 * A219966 A103958 A321696

Adjacent sequences: A116449 A116450 A116451 * A116453 A116454 A116455

Keyword

nonn

Author

Reinhard Zumkeller, Feb 16 2006

Status

approved