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A243129
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a(n) = sigma(d(d(d(n)))), where d(n) is the number of divisors of n.
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1
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1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 4, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 7, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 7, 3, 3, 4, 4, 3, 4, 3, 4, 3, 3, 3, 7, 3, 3
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OFFSET
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1,2
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COMMENTS
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a(n) >= 3 for n > 1 with a(1) = 1. If n is a prime or a semiprime, a(n) = 3. The converse is not true since a(8) = 3, but 8 is neither a prime nor a semiprime.
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LINKS
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FORMULA
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EXAMPLE
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a(12) = 4; 12 has 6 divisors --> 6 has 4 divisors --> 4 has 3 divisors --> and the sum of the divisors of 3 is 4.
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MAPLE
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with(numtheory); A243129:=n->sigma(tau(tau(tau(n)))); seq(A243129(n), n=1..100);
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MATHEMATICA
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Table[DivisorSigma[1, DivisorSigma[0, DivisorSigma[0, DivisorSigma[0, n]]]], {n, 100}]
Table[DivisorSigma[1, Nest[DivisorSigma[0, #]&, n, 3]], {n, 100}] (* Harvey P. Dale, Mar 24 2016 *)
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CROSSREFS
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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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