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 A353955 #12 Aug 05 2022 22:27:11
%S A353955 1,2,3,5,7,6,11,35,13,22,15,91,17,10,21,143,34,105,19,26,33,85,14,39,
%T A353955 55,119,78,95,77,51,65,154,57,221,70,209,663,23,110,273,323,46,165,
%U A353955 1547,38,69,385,442,437,231,130,391,133,30,187,247,42,935,299,114,595
%N A353955 a(n) = A019565(A353709(n)).
%C A353955 Interpretation of A353709(n) written in binary instead as if written in "multiplicity notation", that is, as if we write 1 if divisible by prime(k+1), otherwise 0 in the k-th place. Example, decimal 12 is written in binary as 1100 = 2^2 + 2^3, and take exponents 2 and 3 and instead construe them as prime(2+1) * prime(3+1) = 5*7 = 35.
%C A353955 If A353709 is a permutation of nonnegative numbers, then this sequence is a permutation of squarefree numbers A005117.
%H A353955 Michael De Vlieger, <a href="/A353955/b353955.txt">Table of n, a(n) for n = 0..10000</a>
%H A353955 Michael De Vlieger, <a href="/A353955/a353955.png">Annotated log log scatterplot of a(n)</a>, n = 1..2^14, with records in red and local minima in blue, highlighting primes in green and fixed points in gold.
%F A353955 a(n) = Product p_k where A353709(n) = Sum 2^(k-1).
%e A353955 Table showing n, A353709(n), and b(n), the binary expansion of A353709(n) writing "." for zeros for clarity. a(n) interprets 1's in the k-th place of b(n) as prime(k+1) and thereafter takes the product. We find a(n) = A005117(j).
%e A353955 n A353709(n) b(n) a(n) j
%e A353955 ----------------------------
%e A353955 1 0 . 1 1
%e A353955 2 1 1 2 2
%e A353955 3 2 1. 3 3
%e A353955 4 4 1.. 5 4
%e A353955 5 8 1... 7 6
%e A353955 6 3 11 6 5
%e A353955 7 16 1.... 11 8
%e A353955 8 12 11.. 35 23
%e A353955 9 32 1..... 13 9
%e A353955 10 17 1...1 22 15
%e A353955 11 6 11. 15 11
%e A353955 12 40 1.1... 91 57
%e A353955 13 64 1...... 17 12
%e A353955 14 5 1.1 10 7
%e A353955 15 10 1.1. 21 14
%e A353955 16 48 11.... 143 89
%e A353955 ...
%t A353955 nn = 2^7; c[_] = -1; c[0] = i = 0; a[0] = c[1] = j = 1; a[1] = u = 2; Do[k = u; While[Nand[c[k] == -1, BitAnd[i, k] == 0, BitAnd[j, k] == 0], k++]; If[k == u, While[c[u] > -1, u++]]; i = j; j = k; Set[{a[n], c[k]}, {Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, Reverse@ IntegerDigits[k, 2]], n}], {n, 2, nn}]; Array[a, nn + 1, 0]
%Y A353955 Cf. A005117, A019565, A353709.
%K A353955 nonn
%O A353955 0,2
%A A353955 _Michael De Vlieger_, May 12 2022