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A360330
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a(n) is the number of divisors of n that have only prime factors that are not prime-indexed primes.
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3
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1, 2, 1, 3, 1, 2, 2, 4, 1, 2, 1, 3, 2, 4, 1, 5, 1, 2, 2, 3, 2, 2, 2, 4, 1, 4, 1, 6, 2, 2, 1, 6, 1, 2, 2, 3, 2, 4, 2, 4, 1, 4, 2, 3, 1, 4, 2, 5, 3, 2, 1, 6, 2, 2, 1, 8, 2, 4, 1, 3, 2, 2, 2, 7, 2, 2, 1, 3, 2, 4, 2, 4, 2, 4, 1, 6, 2, 4, 2, 5, 1, 2, 1, 6, 1, 4, 2
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OFFSET
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1,2
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COMMENTS
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Equivalently, a(n) is the number of divisors of the largest divisor of n that has only prime factors that are not prime-indexed primes.
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LINKS
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FORMULA
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a(n) = 1 if and only if n is in A076610.
Multiplicative with a(p^e) = 1 if p is a prime-indexed prime (A006450), and e+1 otherwise (A007821).
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MAPLE
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a:= n-> mul(`if`(isprime(numtheory[pi](i[1])), 1, i[2]+1), i=ifactors(n)[2]):
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MATHEMATICA
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f[p_, e_] := If[PrimeQ[PrimePi[p]], 1, e+1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PROG
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(PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(isprime(primepi(p[i])), 1, e[i]+1)); }
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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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