Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #24 Sep 16 2023 11:36:38
%S 7,35,193,1280,9700,78734,665134,5762859,50851223,455062595,
%T 4118082969,37607992088,346065767406,3204942420923,29844572385358,
%U 279238346816392,2623557174778438,24739954338671299,234057667428388198,2220819603016308079,21127269487386615271,201467286693435354626,1925320391619238700024,18435599767386814628355,176846309399257764978954,1699246750872783231673649
%N Number of nontrivial prime powers p^k (k > 0) less than 10^n.
%C This is the sum of A006880 and A267574, term by term.
%F a(n) = A006880(n) + A267574(n).
%F a(n) = A238815(n) - 1. - _Jon E. Schoenfield_, Apr 19 2018
%e For n=1, there are 4 primes plus 3 prime powers less than 10^1: 2, 3, 4, 5, 7, 8, 9; 7 in total.
%t Table[Count[Range[10^n], k_ /; PrimePowerQ@ k], {n, 6}] (* _Michael De Vlieger_, Jan 20 2016 *)
%t f[n_] := Sum[PrimePi[10^(n/k)], {k, n*Log2[10]}]; Array[f, 14] (* _Robert G. Wilson v_, Aug 17 2017, after _Giovanni Resta_ in A267574 *)
%o (SageMath)
%o def A267712(n):
%o gen = (p for p in srange(2, 10^n) if p.is_prime_power())
%o return sum(1 for _ in gen)
%o print([A267712(n) for n in range(1, 7)]) # _Peter Luschny_, Sep 16 2023
%Y Cf. A006880, A238815, A267574, A089579.
%K nonn
%O 1,1
%A _Daniel Mondot_, Jan 19 2016
%E a(20)-a(26) from _Chai Wah Wu_, Jan 25 2016