A124831 Number of prime factors of A055932(n) with repetition.

0, 1, 2, 2, 3, 3, 4, 3, 4, 3, 5, 4, 5, 4, 4, 6, 5, 4, 6, 5, 5, 7, 6, 4, 5, 5, 7, 4, 6, 6, 8, 5, 7, 5, 6, 6, 8, 5, 7, 5, 7, 6, 9, 6, 8, 6, 5, 7, 7, 5, 9, 6, 6, 8, 6, 8, 7, 10, 5, 7, 9, 7, 6, 8, 6, 8, 7, 5, 6, 10, 7, 7, 9, 7, 6, 9, 8, 11, 6, 8, 6, 10, 5, 8, 7, 7, 9, 7, 9, 8, 6, 7, 11, 6, 8, 8, 10, 8, 6, 7, 10

Offset

0,3

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Formula

a(n) = A001222(A055932(n)).

Mathematica

Map[PrimeOmega, {1}~Join~Select[Range[10^4], Last[#] == Length[#] &@ PrimePi@ FactorInteger[#][[All, 1]] &]] (* Michael De Vlieger, Feb 06 2020 *)

Prog

(Python)
from itertools import count
from functools import lru_cache
from sympy import prime, integer_log, primorial, primeomega
from oeis_sequences.OEISsequences import bisection
def A124831(n):
    @lru_cache(maxsize=None)
    def g(x, m): return sum(g(x//(prime(m)**i), m-1) for i in range(1, integer_log(x, prime(m))[0]+1)) if m-1 else x.bit_length()-1
    def f(x):
        c = n-1+x
        for k in count(1):
            if primorial(k)>x:
                break
            c -= g(x, k)
        return c
    return primeomega(bisection(f, n, n)) # Chai Wah Wu, Mar 21 2026

Crossrefs

Cf. A055932, A001222, A124829, A124831, A036041.

Sequence in context: A057935 A292042 A282715 * A157790 A070241 A066412

Adjacent sequences: A124828 A124829 A124830 * A124832 A124833 A124834

Keyword

nonn

Author

Franklin T. Adams-Watters, Nov 09 2006

Status

approved