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3, 8, 24, 80, 288, 1088, 4224, 4374, 16640, 66048, 263168, 1050624, 4198400
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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For every k >= 0, the sequence includes 4^k + 2^(k+1), with m = 2^k + 1. - David Wasserman, Jan 29 2004
Are there other terms like 4374 that are not of this form? - Michel Marcus, Aug 10 2014
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LINKS
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FORMULA
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G.f.: Conjecture: Q(0)/x - 1/x where Q(k)= 1 + 2^k*x/(1 - 2*x/(2*x + 2^k*x/Q(k+1) )); (continued fraction ). - Sergei N. Gladkovskii, Apr 10 2013
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EXAMPLE
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With n=3 and m=2, rad(3) = rad(3) and rad(2) = rad(4), so 3 is in the sequence.
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MAPLE
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rad:= n -> convert(numtheory:-factorset(n), `*`):
count:= 0: lastr:= rad(1):
for n from 2 to 10^7 do
newr:= rad(n);
P[lastr, newr]:= n-1;
if assigned(P[newr, lastr]) then
count:= count+1; A[count]:= n-1; M[count]:= P[newr, lastr];
fi;
lastr:= newr;
od:
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MATHEMATICA
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(* Recomputation up to a(13), assuming m of the form 2^k+1 *)
rad[n_] := rad[n] = Select[Divisors[n], SquareFreeQ][[-1]];
okQ[n_] := Module[{r = rad[n], r1 = rad[n+1], k, m}, For[k = 0, k < Log[2, n-1], k++, m = 2^k+1; If[r == rad[m+1] && rad[m] == r1, Return[True]]]; False];
Reap[For[n = 1, n <= 5*10^6, n++, If[okQ[n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Apr 11 2019 *)
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PROG
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(PARI) lista(nn) = {v = vector(nn, i, rad(i)); for (n=1, nn-1, ok = 0; if (n % 2, ma = 2, ma = 1); forstep (m = ma, n-1, 2, if ((v[n] == v[m+1]) && (v[m] == v[n+1]), ok = 1; break); ); if (ok, print1(n, ", ")); ); } \\ Michel Marcus, Aug 10 2014
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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