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]
PROG
(PARI) a(n) = vecprod(apply(x -> if(x == 3 || x == 6, 4, 2), factor(n)[, 2])); \\ Amiram Eldar, Dec 18 2023
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Jun 04 2020
STATUS
approved