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%I #23 Sep 17 2023 06:01:36
%S 0,1,14,72,257,873,2838,9085,28979,92145,292832,930124,2953569,
%T 9376798,29760901,94434276,299569798,950072891,3012393832,9549260877,
%U 30264906899,95902117819,303839485659,962486295193,3048497625289,9654373954803,30571355398031,96797106918709
%N Number of perfect powers k which are not prime powers, and 1 < k < 10^n.
%C k is a perfect power (A001597) <=> there exist integers m and b, b > 1, m >= 1, and k = m^b.
%C k is a prime power (A246655) <=> there exist integers p and b, b >= 1, p is a prime, and k = p^b.
%H Plot2, <a href="https://oeis.org/plot2a?name1=A267574&name2=A089579&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawlines=true">A267574(n)/A089579(n)</a>.
%F a(n) = A089579(n) - A267574(n).
%F a(n) = card({k: 1 < k < 10^n and k in A131605}).
%F If k = m^b is a term counted by this sequence then base(k) = m is a term of A024619.
%e There are 14 perfect powers less than 1000 which are not prime powers:
%e 6^2, 10^2, 12^2, 14^2, 6^3, 15^2, 18^2, 20^2, 21^2, 22^2, 24^2, 26^2, 28^2, 30^2.
%o (SageMath)
%o def A365670(n):
%o gen = (p for p in srange(2, 10^n)
%o if p.is_perfect_power() and not p.is_prime_power())
%o return sum(1 for _ in gen)
%o print([A365670(n) for n in range(1, 7)])
%Y Cf. A089579, A267574, A131605, A001597, A246655, A024619.
%K nonn
%O 1,3
%A _Peter Luschny_, Sep 16 2023
%E Data based on A089579 and A267574.
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