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A330944
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Number of nonprime prime indices of n.
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20
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0, 1, 0, 2, 0, 1, 1, 3, 0, 1, 0, 2, 1, 2, 0, 4, 0, 1, 1, 2, 1, 1, 1, 3, 0, 2, 0, 3, 1, 1, 0, 5, 0, 1, 1, 2, 1, 2, 1, 3, 0, 2, 1, 2, 0, 2, 1, 4, 2, 1, 0, 3, 1, 1, 0, 4, 1, 2, 0, 2, 1, 1, 1, 6, 1, 1, 0, 2, 1, 2, 1, 3, 1, 2, 0, 3, 1, 2, 1, 4, 0, 1, 0, 3, 0, 2, 1
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OFFSET
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1,4
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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FORMULA
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Additive with a(p^e) = e if primepi(p) is nonprime, and 0 otherwise. - Amiram Eldar, Nov 03 2023
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EXAMPLE
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24 has prime indices {1,1,1,2}, of which {1,1,1} are nonprime, so a(24) = 3.
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MATHEMATICA
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Table[Total[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}/; !PrimeQ[PrimePi[p]]:>k]], {n, 30}]
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PROG
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(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if(!isprime(primepi(f[k, 1])), f[k, 2], 0)); \\ Daniel Suteu, Jan 14 2020
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CROSSREFS
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The number of prime prime indices is given by A257994.
Primes of nonprime index are A007821.
Products of primes of prime index are A076610.
Products of primes of nonprime index are A320628.
Numbers whose prime indices are not all prime are A330945.
Cf. A000040, A000720, A001222, A007097, A018252, A056239, A112798, A302242, A320629, A320633, A330946, A330947.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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