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Sum {k = 1..n} tau(k) is a prime, where tau is the Ramanujan tau function (A000594).
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%I #4 Dec 22 2015 11:19:50

%S 2,3,39,97,172,177,200,203,318,332,345,500,519,527,651,660,722,865,

%T 870,881,890,897,1089,1091,1101,1106,1156,1177,1192,1205,1369,1370,

%U 1393,1425,1459,1466,1499,1500,1503,1505,1517,1519,1703,1755,1779,1782,1786

%N Sum {k = 1..n} tau(k) is a prime, where tau is the Ramanujan tau function (A000594).

%t Needs["NumberTheory`Ramanujan`"]; s = 0; Do[s = s + RamanujanTau[n]; If[PrimeQ[s], Print[n]], {n, 1, 10^4}]

%t Flatten[Position[Accumulate[RamanujanTau[Range[0,1800]]],_?(PrimeQ[ #]&)]]-1 (* _Harvey P. Dale_, Dec 22 2015 *)

%Y Cf. A000594.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Dec 30 2002