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

Author

Leroy Quet, Jun 16 2008

Keywords

• nonn

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

Crossrefs

Cf. A000005, A139118, A141242.

Programs

Mathematica

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

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

Formula

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

Extensions

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