

A335385


The number of triunitary divisors of n.


3



1, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 8, 2, 4, 4, 4, 2, 8, 2, 2, 4, 4, 4, 4, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 8, 4, 8, 4, 4, 2, 8, 2, 4, 4, 4, 4, 8, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 4, 8, 2, 4, 2, 4, 2, 8, 4, 4, 4
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OFFSET

1,2


COMMENTS

A divisor d of k is triunitary if the greatest common biunitary divisor of d and k/d is 1.
Differs from A037445 at n = 32, 96, 128, 160, 224, ...


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Graeme L. Cohen, On an integer's infinitary divisors, Mathematics of Computation, Vol. 54, No. 189 (1990), pp. 395411.
Pentti Haukkanen, On the kary convolution of arithmetical functions, The Fibonacci Quarterly, Vol. 38, No. 5 (2000) pp. 440445.


FORMULA

Multiplicative with a(p^e) = 4 if e = 3 or 6, and a(p^e) = 2 otherwise.


EXAMPLE

a(4) = 2 since 4 has 2 triunitary divisors, 1 and 4. 2 is not a triunitary divisor of 4 since the greatest common biunitary divisor of 2 and 4/2 = 2 is 2 and not 1.


MATHEMATICA

f[p_, e_] := If[e == 3  e == 6, 4, 2]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100]


CROSSREFS

Cf. A222266, A324706, A324707, A324708, A324709.
Cf. A000005, A034444, A037445, A048105, A049419, A286324, A322483.
Sequence in context: A084718 A154851 A281854 * A037445 A318307 A331109
Adjacent sequences: A335382 A335383 A335384 * A335386 A335387 A335388


KEYWORD

nonn,mult


AUTHOR

Amiram Eldar, Jun 04 2020


STATUS

approved



