This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335385 #17 Jan 05 2025 19:51:41 %S A335385 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, %T A335385 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, %U A335385 4,8,2,8,2,4,4,4,4,8,2,4,2,4,2,8,4,4,4 %N A335385 The number of tri-unitary divisors of n. %C A335385 A divisor d of k is tri-unitary if the greatest common bi-unitary divisor of d and k/d is 1. %C A335385 Differs from A037445 at n = 32, 96, 128, 160, 224, ... %H A335385 Amiram Eldar, <a href="/A335385/b335385.txt">Table of n, a(n) for n = 1..10000</a> %H A335385 Graeme L. Cohen, <a href="https://doi.org/10.1090/S0025-5718-1990-0993927-5">On an integer's infinitary divisors</a>, Mathematics of Computation, Vol. 54, No. 189 (1990), pp. 395-411. %H A335385 Pentti Haukkanen, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/38-5/haukkanen.pdf">On the k-ary convolution of arithmetical functions</a>, The Fibonacci Quarterly, Vol. 38, No. 5 (2000), pp. 440-445. %F A335385 Multiplicative with a(p^e) = 4 if e = 3 or 6, and a(p^e) = 2 otherwise. %e A335385 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. %t A335385 f[p_, e_] := If[e == 3 || e == 6, 4, 2]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] %o A335385 (PARI) a(n) = vecprod(apply(x -> if(x == 3 || x == 6, 4, 2), factor(n)[, 2])); \\ _Amiram Eldar_, Dec 18 2023 %Y A335385 Cf. A222266, A324706, A324707, A324708, A324709. %Y A335385 Cf. A000005, A034444, A037445, A048105, A049419, A286324, A322483. %K A335385 nonn,easy,mult %O A335385 1,2 %A A335385 _Amiram Eldar_, Jun 04 2020