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%I #15 Apr 04 2024 03:04:34
%S 1,2,3,4,5,6,7,8,9,15,16,17,18,19,28,29,30,31,32,33,75,76,77,78,79,80,
%T 81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,125,126,127,
%U 128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144
%N Let D(n,s) denotes the denominator of Sum_{k=1..n} 1/k^s; sequence gives values of n such that D(n,4)/D(n,2) is a perfect square.
%H Robert Israel, <a href="/A069118/b069118.txt">Table of n, a(n) for n = 1..3952</a>
%e 3 is in the sequence because 1/1^4 +1/2^4 + 1/3^4 = 1393/1296 and 1/1^2 + 1/2^2 + 1/3^2 = 49/36, and 1296/36 = 36 = 6^2.
%p dd:= (n,s) -> denom(add(1/k^s,k=1..n)):
%p select(t -> issqr(dd(t,4)/dd(t,2)), [$1..1000]); # _Robert Israel_, May 18 2014
%o (PARI) default(realprecision, 1000); for(n=1,300,if(sqrt(denominator(sum(i=1,n,1/i^4))/denominator(sum(i=1,n,1/i^2))) == floor(sqrt(denominator(sum(i=1,n,1/i^4))/denominator(sum(i=1,n,1/i^2)))),print1(n,",")))
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Apr 07 2002