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 A353954 #18 Jul 01 2025 08:56:13
%S A353954 1,2,3,5,6,7,10,21,11,15,14,33,35,22,105,13,30,77,26,55,42,65,66,91,
%T A353954 110,39,70,143,210,17,165,182,51,154,195,34,231,130,119,330,221,462,
%U A353954 85,78,385,102,455,187,390,1309,19,770,663,38,1155,442,57,910,561,95,273
%N A353954 a(0) = 1; a(n) = A019565(A109812(n)).
%C A353954 Interpretation of A109812(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 A353954 Permutation of squarefree numbers A005117.
%H A353954 Michael De Vlieger, <a href="/A353954/b353954.txt">Table of n, a(n) for n = 0..10000</a>
%H A353954 Michael De Vlieger, <a href="/A353954/a353954.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 A353954 a(0) = 1; a(n) = Product p_k where A109812(n) = Sum 2^(k-1) for n > 0.
%e A353954 Table showing n, A109812(n), and b(n), the binary expansion of A109812(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). Note that A109812(0) is not defined.
%e A353954 n A109812(n) b(n) a(n) j
%e A353954 ----------------------------
%e A353954 0 - . 1 1
%e A353954 1 1 1 2 2
%e A353954 2 2 1. 3 3
%e A353954 3 4 1.. 5 4
%e A353954 4 3 11 6 5
%e A353954 5 8 1... 7 6
%e A353954 6 5 1.1 10 7
%e A353954 7 10 1.1. 21 14
%e A353954 8 16 1.... 11 8
%e A353954 9 6 11. 15 11
%e A353954 10 9 1..1 14 10
%e A353954 11 18 1..1. 33 21
%e A353954 12 12 11.. 35 23
%e A353954 13 17 1...1 22 15
%e A353954 14 14 111. 105 65
%e A353954 15 32 1..... 13 9
%e A353954 16 7 111 30 19
%e A353954 ...
%t A353954 Clear[c, a]; nn = 60; c[_] = 0; a[0] = c[1] = j = 1; a[1] = u = 2; Do[k = u; While[Nand[c[k] == 0, BitAnd[j, k] == 0], k++]; If[k == u, While[c[u] > 0, u++]]; j = k; Set[{a[i], c[k]}, {Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, Reverse@ IntegerDigits[k, 2]], i}], {i, 2, nn}]; Array[a, nn + 1, 0]
%Y A353954 Cf. A005117, A019565, A109812.
%K A353954 nonn
%O A353954 0,2
%A A353954 _Michael De Vlieger_, May 12 2022