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 A372133 #7 May 12 2024 11:17:51
%S A372133 0,1,2,3,4,7,8,5,6,14,16,13,32,28,56,9,64,26,128,52,112,224,256,19,12,
%T A372133 448,10,104,512,25,1024,11,896,1792,3584,23,2048,7168,14336,38,4096,
%U A372133 50,8192,208,416,28672,16384,31,24,832,57344,1664,32768,76,114688
%N A372133 Prime shadow (A181819) with shifted e_i to generate odd numbers, multiplied by 2^(A064839 - 1).
%C A372133 a(n>1) contains all positive integers exactly once.
%F A372133 Factor n, multiplying out prime(e_i + 1) generates all odd numbers >= 3. Subtract 2 and multiply by 2^(k - 1), where k is the number of occurrences of the same prime signature of n in (1..n) (A064839).
%t A372133 z = 100; prisigs = Table[If[n == 1, {0}, Sort[Last /@ FactorInteger[n]]], {n, z}];
%t A372133 exps = Table[Count[Take[prisigs, n], prisigs[[n]]], {n, z}]; (*A064839*)
%t A372133 Table[2^(exps[[n]] - 1) (Times @@ Prime[1 + prisigs[[n]]] - 2), {n, z}]
%Y A372133 Cf. A064839, A181819, A372134.
%K A372133 nonn
%O A372133 1,3
%A A372133 _Friedjof Tellkamp_, Apr 20 2024