

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
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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



