A372134 Prime shadows (A181819) linearly transformed to generate odd numbers, multiplied by 2^(A064839 - 1).

-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, 320, 14, 72, 512, 13, 1024, 19, 640, 1280, 2560, 15, 2048, 5120, 10240, 34, 4096, 26, 8192, 144, 288, 20480, 16384, 25, 24, 576, 40960, 1152, 32768, 68, 81920, 136

Offset

1,3

Comments

a(n>1) contains all positive integers exactly once.

Links

Table of n, a(n) for n=1..56.

Formula

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).

Mathematica

z = 100; prisigs = Table[If[n == 1, {}, Sort[Last /@ FactorInteger[n]]], {n, z}];
exps = Table[Count[Take[prisigs, n], prisigs[[n]]], {n, z}]; (* A064839 *)
Table[2^(exps[[n]] - 1) (2 Times @@ Prime[prisigs[[n]]] - 3), {n, z}]

Crossrefs

Cf. A064839, A181819, A372133.

Sequence in context: A249813 A246683 A332816 * A354732 A094607 A258831

Adjacent sequences: A372131 A372132 A372133 * A372135 A372136 A372137

Keyword

sign

Author

Friedjof Tellkamp, Apr 20 2024

Status

approved