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A189715
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Numbers k such that A156595(k-1) = 0; complement of A189716.
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10
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1, 4, 6, 7, 9, 10, 13, 15, 16, 19, 22, 24, 25, 28, 31, 33, 34, 36, 37, 40, 42, 43, 46, 49, 51, 52, 54, 55, 58, 60, 61, 63, 64, 67, 69, 70, 73, 76, 78, 79, 81, 82, 85, 87, 88, 90, 91, 94, 96, 97, 100, 103, 105, 106, 109, 112, 114, 115, 117, 118, 121, 123, 124, 127, 130, 132, 133, 135, 136, 139, 141, 142, 144, 145, 148, 150, 151, 154, 157, 159
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OFFSET
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1,2
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COMMENTS
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Numbers whose squarefree part is congruent modulo 9 to 1, 4, 6 or 7. - Peter Munn, May 17 2020
The asymptotic density of this sequence is 1/2. - Amiram Eldar, Mar 08 2021
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LINKS
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MATHEMATICA
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t = Nest[Flatten[# /. {0->{0, 1, 1}, 1->{0, 1, 0}}] &, {0}, 5] (*A156595*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (*A189715*)
Flatten[Position[t, 1]] (*A189716*)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189717*)
f[p_, e_] := (p^Mod[e, 2]); sqfpart[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[160], MemberQ[{1, 4, 6, 7}, Mod[sqfpart[#], 9]] &] (* Amiram Eldar, Mar 08 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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