|
| |
|
|
A335385
|
|
The number of tri-unitary 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
A divisor d of k is tri-unitary if the greatest common bi-unitary 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. 395-411.
Pentti Haukkanen, On the k-ary convolution of arithmetical functions, The Fibonacci Quarterly, Vol. 38, No. 5 (2000) pp. 440-445.
|
|
|
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 tri-unitary divisors, 1 and 4. 2 is not a tri-unitary divisor of 4 since the greatest common bi-unitary 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
|
| |
|
|
