A105998 Semiprime function n -> A001358(n) applied four times to n.

77, 119, 219, 235, 377, 381, 566, 634, 721, 779, 998, 1006, 1126, 1282, 1294, 1563, 1642, 1745, 1853, 1959, 1961, 2209, 2402, 2483, 2554, 2785, 3005, 3149, 3173, 3242, 3481, 3574, 3587, 3622, 4101, 4282, 4471, 4681, 4714, 4798, 4859, 4882, 5095, 5201

Offset: 1

Author

Jonathan Vos Post, Apr 29 2005

Keywords

• easy
• nonn

Examples

			a(1) = semiprime(semiprime(semiprime(semiprime(1)))) = semiprime(semiprime(semiprime(4))) = semiprime(semiprime(10)) = semiprime(26) = 77.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A007097, A091022, A105997, A105999.

Programs

Maple

issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:
sp:= proc(n) option remember; local k; if n=1 then 4 else
       for k from 1+sp(n-1) while not issp(k) do od; k fi end:
a:= n-> (sp@@4)(n):
seq(a(n), n=1..44);  # Alois P. Heinz, Aug 16 2024

Mathematica

f[n_] := Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[ n]]; t = Select[ Range[ 5210], f[ # ] == 2 &]; Table[ Nest[ t[[ # ]] &, n, 4], {n, 45}] (* Robert G. Wilson v, Apr 30 2005 *)

Python

from math import isqrt
from sympy import primepi, primerange
def A105998(n):
    def f(x): return int(x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//k) for k in primerange(1, s+1)))
    def A001358(n):
        m, k = n, f(n)+n
        while m != k:
            m, k = k, f(k)+n
        return m
    return A001358(A001358(A001358(A001358(n)))) # Chai Wah Wu, Aug 16 2024

Formula

a(n) = A001358(A001358(A001358(A001358(n)))).

Extensions

More terms from Robert G. Wilson v, Apr 30 2005