

A085459


Numbers k such that kth cyclotomic polynomial has exactly 3 positive coefficients.


1



3, 9, 10, 20, 27, 40, 50, 80, 81, 100, 160, 200, 243, 250, 320, 400, 500, 640, 729, 800, 1000, 1250, 1280, 1600, 2000, 2187, 2500, 2560, 3200, 4000, 5000, 5120, 6250, 6400, 6561, 8000, 10000, 10240, 12500, 12800, 16000, 19683, 20000, 20480, 25000, 25600
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OFFSET

1,1


COMMENTS

Sequence appears to consist of 3^i, i > 0; and 2^i*5^j, i, j > 0. Are there any other terms?  David Wasserman, Feb 01 2005
It appears they are the solutions of the equation x = phi(x)/2 + phi(2*x).  Paolo P. Lava, Oct 26 2017


LINKS

Table of n, a(n) for n=1..46.


EXAMPLE

9 is a member because the 9th cyclotomic polynomial is P(x) = x^6+x^3+1.


MAPLE

with(numtheory): P:=proc(n) local x;
if nops(select(x>x>0, [coeffs(cyclotomic(n, x))]))=3 then n; fi;
end: seq(P(j), j=1..25600); # Paolo P. Lava, Oct 26 2017


MATHEMATICA

Select[Range@ 5000, Count[CoefficientList[Cyclotomic[#, x], x], _?(# > 0 &)] == 3 &] (* Michael De Vlieger, Oct 26 2017 *)


PROG

(PARI) n = 0; while (1, n++; p = polcyclo(n, x); d = poldegree(p); c = 0; i = 0; while (c < 4 && i <= d, if (polcoeff(p, i) > 0, c++); i++); if (c == 3, print(n))); \\ David Wasserman, Feb 01 2005


CROSSREFS

Cf. A065119, A086765.
Sequence in context: A134073 A088005 A125237 * A092169 A093108 A247519
Adjacent sequences: A085456 A085457 A085458 * A085460 A085461 A085462


KEYWORD

nonn,easy


AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 14 2003


EXTENSIONS

More terms from David Wasserman, Feb 01 2005


STATUS

approved



