cp's OEIS Frontend

A085971 Union of primes and numbers that are not prime powers (A000040, A024619).

%I A085971 #12 Aug 20 2024 13:19:50
%S A085971 2,3,5,6,7,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,28,29,30,31,
%T A085971 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,50,51,52,53,54,55,56,
%U A085971 57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78
%N A085971 Union of primes and numbers that are not prime powers (A000040, A024619).
%C A085971 Complement of A025475;
%C A085971 A085972(n) = Max{k: a(k)<=n};
%C A085971 different from A007916 and A052485, as a(28)=36;
%C A085971 A085818(a(n)) = A000040(n).
%F A085971 a(n) = n + o(sqrt n). - _Charles R Greathouse IV_, Oct 19 2015
%t A085971 With[{nn=100},Union[Join[Prime[Range[PrimePi[nn]]],DeleteCases[Range[2,80], _?(PrimePowerQ[#]&)]]]] (* _Harvey P. Dale_, May 15 2019 *)
%o A085971 (PARI) is(n)=isprimepower(n)<2 && n>1 \\ _Charles R Greathouse IV_, Oct 19 2015
%o A085971 (Python)
%o A085971 from sympy import primepi, integer_nthroot
%o A085971 def A085971(n):
%o A085971     def f(x): return int(n+sum(primepi(integer_nthroot(x,k)[0]) for k in range(2,x.bit_length())))
%o A085971     kmin, kmax = 1,2
%o A085971     while f(kmax) >= kmax:
%o A085971         kmax <<= 1
%o A085971     while True:
%o A085971         kmid = kmax+kmin>>1
%o A085971         if f(kmid) < kmid:
%o A085971             kmax = kmid
%o A085971         else:
%o A085971             kmin = kmid
%o A085971         if kmax-kmin <= 1:
%o A085971             break
%o A085971     return kmax # _Chai Wah Wu_, Aug 20 2024
%K A085971 nonn,easy
%O A085971 1,1
%A A085971 _Reinhard Zumkeller_, Jul 06 2003