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A243129 a(n) = sigma(d(d(d(n)))), where d(n) is the number of divisors of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A000203(A000005(A000005(A000005(n)))).

EXAMPLE

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.

MAPLE

with(numtheory); A243129:=n->sigma(tau(tau(tau(n)))); seq(A243129(n), n=1..100);

MATHEMATICA

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 *)

CROSSREFS

Cf. A000005, A000203.

Sequence in context: A087717 A053444 A175797 * A135717 A079083 A176171

Adjacent sequences:  A243126 A243127 A243128 * A243130 A243131 A243132

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, May 29 2014

STATUS

approved

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Last modified May 25 06:42 EDT 2020. Contains 334581 sequences. (Running on oeis4.)