A141241 a(n) = number of divisors of n-th positive integer with a nonprime number of divisors. a(n) = the number of divisors of A139118(n).

1, 4, 4, 4, 6, 4, 4, 6, 6, 4, 4, 8, 4, 4, 6, 8, 6, 4, 4, 4, 9, 4, 4, 8, 8, 6, 6, 4, 10, 6, 4, 6, 8, 4, 8, 4, 4, 12, 4, 6, 4, 8, 6, 4, 8, 12, 4, 6, 6, 4, 8, 10, 4, 12, 4, 4, 4, 8, 12, 4, 6, 4, 4, 4, 12, 6, 6, 9, 8, 8, 8, 4, 12, 8, 4, 10, 8, 4, 6, 6, 4, 4, 16, 4, 4, 6, 4, 12, 8, 4, 8, 12, 4, 4, 8, 8, 8, 12, 4

Offset

1,2

Comments

a(1) = 1 and all other terms are composite, of course.

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(A139118(n)). - Michel Marcus, Feb 26 2025

Mathematica

Select[DivisorSigma[0, Range[200]], !PrimeQ[#]&] (* Harvey P. Dale, Mar 20 2015 *)

Prog

(PARI) for(i=1, 200, if(!isprime(numdiv(i)), print1(numdiv(i)", "))) \\ Franklin T. Adams-Watters, Apr 09 2009
(Python)
from sympy import primepi, integer_nthroot, primerange, divisor_count
def A141241(n):
    def f(x): return int(n+sum(primepi(integer_nthroot(x, k-1)[0]) for k in primerange(x.bit_length()+1)))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return divisor_count(m) # Chai Wah Wu, Feb 22 2025

Crossrefs

Cf. A000005, A139118, A141242.

Sequence in context: A164821 A348677 A130331 * A140696 A160401 A114742

Adjacent sequences: A141238 A141239 A141240 * A141242 A141243 A141244

Keyword

nonn

Author

Leroy Quet, Jun 16 2008

Extensions

More terms from Franklin T. Adams-Watters, Apr 09 2009

Status

approved