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%I #7 May 12 2024 11:18:08
%S -1,1,2,3,4,5,8,7,6,10,16,9,32,20,40,11,64,18,128,36,80,160,256,17,12,
%T 320,14,72,512,13,1024,19,640,1280,2560,15,2048,5120,10240,34,4096,26,
%U 8192,144,288,20480,16384,25,24,576,40960,1152,32768,68,81920,136
%N Prime shadows (A181819) linearly transformed to generate odd numbers, multiplied by 2^(A064839 - 1).
%C a(n>1) contains all positive integers exactly once.
%F a(n) = (2 * A181819(n) - 3) * 2^(k - 1), where k is the number of occurrences of the same prime signature of n in (1..n) (A064839).
%t z = 100; prisigs = Table[If[n == 1, {}, Sort[Last /@ FactorInteger[n]]], {n, z}];
%t exps = Table[Count[Take[prisigs, n], prisigs[[n]]], {n, z}];(* A064839 *)
%t Table[2^(exps[[n]] - 1) (2 Times @@ Prime[prisigs[[n]]] - 3), {n, z}]
%Y Cf. A064839, A181819, A372133.
%K sign
%O 1,3
%A _Friedjof Tellkamp_, Apr 20 2024
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