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Numbers k such that A066840(k) is a square.
2

%I #11 Feb 03 2021 11:11:34

%S 1,2,3,4,6,8,10,14,16,17,22,26,32,34,38,46,54,58,62,64,74,82,86,94,

%T 106,118,122,128,134,142,146,158,166,171,178,194,202,206,214,218,226,

%U 254,255,256,262,274,278,298,302,314,326,334,346,358,362,382,386,394,398,422,446,451,454,458,466

%N Numbers k such that A066840(k) is a square.

%H Robert Israel, <a href="/A341031/b341031.txt">Table of n, a(n) for n = 1..2500</a>

%e a(6) = 8 is a term because A066840(8) = 4 = 2^2.

%p N:= 1000: # for terms <= N

%p G:= add(numtheory:-mobius(n)*n*x^(2*n)/((1-x^n)*(1-x^(2*n))^2), n=1..N/2):

%p S:= series(G, x, N+1):

%p A66840:= [seq(coeff(S, x, j), j=1..N)]:

%p select(t -> issqr(A66840[t]), [$1..N]);

%Y Includes A000079 and A100484.

%Y Cf. A066840.

%K nonn

%O 1,2

%A _J. M. Bergot_ and _Robert Israel_, Feb 02 2021