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 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

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Last modified March 26 11:46 EDT 2023. Contains 361549 sequences. (Running on oeis4.)