A105998 - OEIS

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

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OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

(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