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

%I A105998 #19 Aug 17 2024 01:34:12
%S A105998 77,119,219,235,377,381,566,634,721,779,998,1006,1126,1282,1294,1563,
%T A105998 1642,1745,1853,1959,1961,2209,2402,2483,2554,2785,3005,3149,3173,
%U A105998 3242,3481,3574,3587,3622,4101,4282,4471,4681,4714,4798,4859,4882,5095,5201
%N A105998 Semiprime function n -> A001358(n) applied four times to n.
%H A105998 Chai Wah Wu, <a href="/A105998/b105998.txt">Table of n, a(n) for n = 1..10000</a>
%F A105998 a(n) = A001358(A001358(A001358(A001358(n)))).
%e A105998 a(1) = semiprime(semiprime(semiprime(semiprime(1)))) = semiprime(semiprime(semiprime(4))) = semiprime(semiprime(10)) = semiprime(26) = 77.
%p A105998 issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:
%p A105998 sp:= proc(n) option remember; local k; if n=1 then 4 else
%p A105998        for k from 1+sp(n-1) while not issp(k) do od; k fi end:
%p A105998 a:= n-> (sp@@4)(n):
%p A105998 seq(a(n), n=1..44);  # _Alois P. Heinz_, Aug 16 2024
%t A105998 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 *)
%o A105998 (Python)
%o A105998 from math import isqrt
%o A105998 from sympy import primepi, primerange
%o A105998 def A105998(n):
%o A105998     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)))
%o A105998     def A001358(n):
%o A105998         m, k = n, f(n)+n
%o A105998         while m != k:
%o A105998             m, k = k, f(k)+n
%o A105998         return m
%o A105998     return A001358(A001358(A001358(A001358(n)))) # _Chai Wah Wu_, Aug 16 2024
%Y A105998 Cf. A001358, A007097, A091022, A105997, A105999.
%K A105998 easy,nonn
%O A105998 1,1
%A A105998 _Jonathan Vos Post_, Apr 29 2005
%E A105998 More terms from _Robert G. Wilson v_, Apr 30 2005