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A360331
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a(n) is the sum of divisors of n that have only prime factors that are not prime-indexed primes.
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5
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1, 3, 1, 7, 1, 3, 8, 15, 1, 3, 1, 7, 14, 24, 1, 31, 1, 3, 20, 7, 8, 3, 24, 15, 1, 42, 1, 56, 30, 3, 1, 63, 1, 3, 8, 7, 38, 60, 14, 15, 1, 24, 44, 7, 1, 72, 48, 31, 57, 3, 1, 98, 54, 3, 1, 120, 20, 90, 1, 7, 62, 3, 8, 127, 14, 3, 1, 7, 24, 24, 72, 15, 74, 114, 1
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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 sum 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 (p^(e+1)-1)/(p-1) otherwise (A007821).
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MAPLE
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a:= n-> mul(`if`(isprime(numtheory[pi](i[1])), 1,
(i[1]^(i[2]+1)-1)/(i[1]-1)), i=ifactors(n)[2]):
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MATHEMATICA
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f[p_, e_] := If[PrimeQ[PrimePi[p]], 1, (p^(e+1)-1)/(p-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, (p[i]^(e[i]+1)-1)/(p[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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