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 A358354 #19 Jul 01 2025 23:01:54
%S A358354 1,2,3,4,8,5,7,9,16,27,6,32,25,11,13,12,17,30,18,23,53,59,82,15,74,78,
%T A358354 93,167,35,64,169,24,128,45,21,529,38,3481,164,60,89,57,87,22,79,166,
%U A358354 94,173,339,433,606,105,538,286,391,929,75,406,1335,90,218,1553
%N A358354 a(n) = n for n <= 3. Thereafter a(n) is the least m such that rad(m) = rad(rad(a(n-3)) + rad(a(n-1))) where rad is A007947.
%C A358354 Similar sequence to A358093, though here the definition works between a(n-1) and a(n-3) (skipping a(n-2)) so there is no evident parity pattern, and adjacent pairs are not always coprime.
%C A358354 Conjecture: for n > 60, a(n) is squarefree. - _Michael De Vlieger_, Jul 01 2025
%H A358354 Michael De Vlieger, <a href="/A358354/b358354.txt">Table of n, a(n) for n = 1..1000</a>
%H A358354 Michael De Vlieger, <a href="/A358354/a358354.png">Annotated log log scatterplot of a(n)</a>, n = 1..256, showing primes in red, perfect prime powers in gold, squarefree composites in green, and numbers neither squarefree nor prime powers in blue and purple, where purple represents powerful numbers that are not prime powers.
%e A358354 To find a(4): a(1)=1, a(3)=3 so a(4) is the least m such that rad(n) = rad(rad(1) + rad(3)) = rad(4) = 2. Since 2 has occurred already, a(4) = 4.
%t A358354 Block[{a, c, f, i, j, k, m, p, q, s, nn}, nn = 62; c[_] = False; p[_] = q[_] = 1; f[n_] := Times @@ FactorInteger[n][[All, 1]]; Array[Set[{a[#], c[#]}, {#, True}] &, 3]; Array[(q[#]++; p[#]++) &[f[a[#]] ] &, 3]; Set[{i, j, k}, Array[f[a[#]] &, 3]]; Do[s = f[i + k]; If[PrimeQ[s], m = s^p[s]; p[s]++, m = q[s]; While[Nand[! c[m s], PowerMod[s, s, m] == 0], m++]; m *= s]; q[s]++; Set[{a[n], c[m], i, j, k}, {m, True, j, k, s}], {n, 4, nn}]; Array[a, nn] ] (* _Michael De Vlieger_, Nov 12 2022 *)
%Y A358354 Cf. A007947, A358093.
%K A358354 nonn
%O A358354 1,2
%A A358354 _David James Sycamore_, Nov 11 2022