A105997 - OEIS

%I #18 Aug 16 2024 23:08:55

%S 26,39,74,77,118,119,178,194,219,235,299,301,329,377,381,454,471,502,

%T 535,565,566,634,679,703,721,779,842,886,893,914,973,995,998,1006,

%U 1126,1174,1227,1282,1294,1317,1337,1343,1389,1418,1457,1563,1577,1623,1642

%N Semiprime function n -> A001358(n) applied three times to n.

%H Chai Wah Wu, <a href="/A105997/b105997.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001358(A001358(A001358(n))).

%e a(1) = semiprime(semiprime(semiprime(1))) = semiprime(semiprime(4)) = semiprime(10) = 26.

%p issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:

%p sp:= proc(n) option remember; local k; if n=1 then 4 else

%p        for k from 1+sp(n-1) while not issp(k) do od; k fi end:

%p a:= n-> (sp@@3)(n):

%p seq(a(n), n=1..49);  # _Alois P. Heinz_, Aug 16 2024

%t f[n_] := Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[ n]]; t = Select[ Range[ 1700], f[ # ] == 2 &]; Table[ Nest[ t[[ # ]] &, n, 3], {n, 50}] (* _Robert G. Wilson v_, Apr 30 2005 *)

%o (Python)

%o from math import isqrt

%o from sympy import primepi, primerange

%o def A105997(n):

%o     def f(x,n): return int(n+x+((t:=primepi(s:=isqrt(x)))*(t-1)>>1)-sum(primepi(x//k) for k in primerange(1, s+1)))

%o     def A001358(n):

%o         m, k = n, f(n,n)

%o         while m != k:

%o             m, k = k, f(k,n)

%o         return m

%o     return A001358(A001358(A001358(n))) # _Chai Wah Wu_, Aug 16 2024

%Y Cf. A001358, A007097, A091022, A105998, A105999.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Apr 29 2005

%E Corrected and extended by _Robert G. Wilson v_, Apr 30 2005