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A293449
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Characteristic function for A056166, numbers that have no nonprime exponents present in their prime factorization n = p_1^e_1 * ... * p_k^e_k.
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3
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1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1
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COMMENTS
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After a(1) = 1 numbers such that only primes occur as exponents in their prime factorization.
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LINKS
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FORMULA
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Multiplicative with a(p^e) = A010051(e).
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EXAMPLE
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For n = 4 = 2^2, 2 is prime, thus a(4) = 1.
For n = 12 = 2^2 * 3^1, 2 is prime, but 1 is not, thus a(12) = 0.
For n = 16 = 2^4, 4 is not prime, thus a(16) = 0.
For n = 72 = 2^3 * 3^2, both exponents 3 and 2 are primes, thus a(72) = 1.
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MATHEMATICA
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{1}~Join~Array[Boole[AllTrue[FactorInteger[#][[All, -1]], PrimeQ]] &, 104, 2] (* Michael De Vlieger, Nov 17 2017 *)
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PROG
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(PARI)
vecproduct(v) = { my(m=1); for(i=1, #v, m *= v[i]); m; };
A293449(n) = vecproduct(apply(e -> isprime(e), factorint(n)[, 2]));
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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