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Numbers for which Ramanujan's tau function is negative.
2

%I #19 Jan 21 2019 06:08:44

%S 2,4,6,7,9,10,12,13,17,20,21,22,25,27,30,31,32,35,37,38,39,43,44,45,

%T 46,49,51,53,56,58,59,60,65,66,67,72,75,76,77,82,83,85,89,92,93,94,96,

%U 99,103,104,105,110,111,112,113,114,116,122,125,126,127,129

%N Numbers for which Ramanujan's tau function is negative.

%H G. C. Greubel, <a href="/A079393/b079393.txt">Table of n, a(n) for n = 0..10000</a>

%e A000594(2) = -24, so a(1) = 2.

%t Select[Range[200], RamanujanTau[#] < 0 &] (* _Carl Najafi_, Sep 09 2011 *)

%o (PARI) T(n)=n*(n+1)/2 rtau3(n)=local(y,j); y=0; j=1; while (T(j-1)<n,j++); j--; for (i=1,j,y=y-(-1)^i*(2*i-1)*x^(T(i-1))); y=y^8; polcoeff(y,n-1) for (n=1,100, if (rtau3(n)<0,print1(n",")))

%o (PARI) isok(n) = ramanujantau(n) < 0; \\ _Michel Marcus_, Jan 20 2019

%Y Cf. A079392, A000594.

%K nonn

%O 0,1

%A _Jon Perry_, Jan 06 2003