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%I #11 Feb 07 2021 02:58:43
%S 1,2,3,4,5,6,9,18,25,27,54,81,125,162,243,486,625,729,1458,2187,3125,
%T 4374,6561,13122,15625,19683,39366,59049,78125,118098,177147,354294,
%U 390625,531441,1062882,1594323,1953125,3188646,4782969,9565938,9765625,14348907,28697814
%N Numbers k such that A124446(k) = 1.
%C Numbers k such that A066840(k) and A124440(k) are coprime.
%C Contains all numbers of the forms 3^j, 2*3^j and 5^j.
%C Conjecture: the only term not of one of those forms is 4.
%F A124446(a(n)) = 1.
%e 18 is a term because A066840(18) = 13 and A124440(18) = 41 are coprime.
%p N:= 2*10^4: # 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 filter:= n -> igcd(A66840[n], n*numtheory:-phi(n)/2)=1:
%p filter(1):= true:
%p select(filter, [$1..N]);
%Y Cf. A066840, A124440, A124446.
%K nonn
%O 1,2
%A _J. M. Bergot_ and _Robert Israel_, Feb 02 2021
%E More terms from _Jinyuan Wang_, Feb 07 2021
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