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%I A127061 #19 Jan 03 2024 07:18:48
%S A127061 2,3,5,17,29,31,37,41,97,439,443,449,457,461,463,1009,1013,3163,3167,
%T A127061 3169,3181,3187,3191,3203,3209,3217,3221,3229,4099,4111,4127,4129,
%U A127061 4133,4139,4153,4157,4159,4283,4289,9461,9463,9467,9473,9479,9491,9497,9511
%N A127061 Primes p such that denominator of Sum_{k=1..p-1} 1/k^2 is a square and denominator Sum_{k=1..p-1} 1/k^3 is a cube.
%H A127061 Artur Jasinski & Michel Marcus, <a href="/A127061/b127061.txt">Table of n, a(n) for n = 1..60</a>
%F A127061 Intersection of A127042 and A127046. - _Michel Marcus_, Nov 05 2013
%t A127061 With[{nn=10000},Select[Flatten[Position[Denominator[Thread[{Accumulate[1/ Range[ nn]^2], Accumulate[ 1/Range[nn]^3]}]],_?(IntegerQ[Sqrt[First[#]]] && IntegerQ[Surd[Last[#],3]]&),{1},Heads->False]],PrimeQ]] (* _Harvey P. Dale_, Mar 05 2014 *)
%o A127061 (PARI) lista(nn) = {forprime(p = 2, nn, if (issquare(denominator(sum(k=1, p-1, 1/k^2))) && ispower(denominator(sum(k=1, p-1, 1/k^3)),3), print1(p, ", ")););} \\ _Michel Marcus_, Nov 05 2013
%Y A127061 Cf. A061002, A034602, A127029, A127042, A127043, A127044, A127046, A127047, A127048, A127049, A127051.
%K A127061 nonn
%O A127061 1,1
%A A127061 _Artur Jasinski_, Jan 04 2007
%E A127061 More terms from _Max Alekseyev_, Feb 08 2007
%E A127061 Missing terms in the [9461, 9587] range inserted by _Michel Marcus_, Nov 05 2013

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