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A295665
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Fully multiplicative with a(prime(m)) = prime(k) when m = prime(k), and a(prime(m)) = 1 when m is not a prime.
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4
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1, 1, 2, 1, 3, 2, 1, 1, 4, 3, 5, 2, 1, 1, 6, 1, 7, 4, 1, 3, 2, 5, 1, 2, 9, 1, 8, 1, 1, 6, 11, 1, 10, 7, 3, 4, 1, 1, 2, 3, 13, 2, 1, 5, 12, 1, 1, 2, 1, 9, 14, 1, 1, 8, 15, 1, 2, 1, 17, 6, 1, 11, 4, 1, 3, 10, 19, 7, 2, 3, 1, 4, 1, 1, 18, 1, 5, 2, 1, 3, 16, 13, 23, 2, 21, 1, 2, 5, 1, 12, 1, 1, 22, 1, 3, 2, 1, 1, 20, 9, 1, 14, 1, 1, 6
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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Other identities. For all n >= 1:
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EXAMPLE
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For n = 360 = 2^3 * 3^2 * 5 = prime(1)^3 * prime(2)^2 * prime(3), 1 is not a prime, but 2 and 3 are, thus a(360) = 2^2 * 3 = 12.
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MATHEMATICA
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Table[Times@@Cases[FactorInteger[n], {p_?(PrimeQ[PrimePi[#]]&), k_}:>PrimePi[p]^k], {n, 40}] (* Gus Wiseman, Jan 17 2020 *)
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PROG
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CROSSREFS
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Positions of terms > 1 are A331386.
Primes of nonprime index are A007821.
Products of primes of prime index are A076610.
Products of primes of nonprime index are A320628.
The number of prime prime indices is A257994.
The number of nonprime prime indices is A330944.
Numbers whose prime indices are not all prime are A330945.
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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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