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A062821
Number of divisors of totient of n.
21
1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 3, 6, 4, 4, 4, 5, 4, 6, 4, 6, 4, 4, 4, 6, 6, 6, 6, 6, 4, 8, 5, 6, 5, 8, 6, 9, 6, 8, 5, 8, 6, 8, 6, 8, 4, 4, 5, 8, 6, 6, 8, 6, 6, 8, 8, 9, 6, 4, 5, 12, 8, 9, 6, 10, 6, 8, 6, 6, 8, 8, 8, 12, 9, 8, 9, 12, 8, 8, 6, 8, 8, 4, 8, 7, 8, 8, 8, 8, 8, 12, 6, 12, 4, 12, 6, 12, 8, 12, 8
OFFSET
1,3
LINKS
Florian Luca and Carl Pomerance, On the average number of divisors of the Euler function, Publicationes Mathematicae Debrecen, Vol. 70, No. 1-2 (2007), pp. 125-148.
FORMULA
a(n) = A000005(A000010(n)).
Sum_{k=1..n} a(k) ~ n * exp(c(n) * (log(n)/log(log(n)))^(1/2) * (1 + O(log(log(log(n)))/log(log(n))))), where c(n) is a number in the interval (1/7, 2*sqrt(2))*exp(-gamma/2) and gamma is A001620 (Luca and Pomerance, 2007). - Amiram Eldar, Oct 29 2022
EXAMPLE
The number of divisors of phi(n) can be greater than, less than, or equal to the number of divisors of n:
.
n phi(n) d(phi(n)) d(n)
== ====== ========= ====
10 4 3 < 4
11 10 4 > 2
28 12 6 = 6
MATHEMATICA
Array[DivisorSigma[0, EulerPhi[#]]&, 110] (* Harvey P. Dale, Jul 13 2012 *)
PROG
(PARI) a(n) = numdiv(eulerphi(n)); \\ Harry J. Smith, Aug 11 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Jul 20 2001
EXTENSIONS
Offset corrected by Jaroslav Krizek, Jul 24 2009
Edited by Jon E. Schoenfield, Nov 13 2016
STATUS
approved