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A365670
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Number of perfect powers k which are not prime powers, and 1 < k < 10^n.
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1
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0, 1, 14, 72, 257, 873, 2838, 9085, 28979, 92145, 292832, 930124, 2953569, 9376798, 29760901, 94434276, 299569798, 950072891, 3012393832, 9549260877, 30264906899, 95902117819, 303839485659, 962486295193, 3048497625289, 9654373954803, 30571355398031, 96797106918709
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OFFSET
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1,3
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COMMENTS
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k is a perfect power (A001597) <=> there exist integers m and b, b > 1, m >= 1, and k = m^b.
k is a prime power (A246655) <=> there exist integers p and b, b >= 1, p is a prime, and k = p^b.
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LINKS
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FORMULA
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a(n) = card({k: 1 < k < 10^n and k in A131605}).
If k = m^b is a term counted by this sequence then base(k) = m is a term of A024619.
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EXAMPLE
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There are 14 perfect powers less than 1000 which are not prime powers:
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.
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PROG
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(SageMath)
gen = (p for p in srange(2, 10^n)
if p.is_perfect_power() and not p.is_prime_power())
return sum(1 for _ in gen)
print([A365670(n) for n in range(1, 7)])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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