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A341032 Numbers k such that A124440(k) is a square.

%I A341032 #12 Feb 04 2021 00:04:46
%S A341032 1,2,10,17,469,646,1542,1601,24939,25090,43690,50925,77577,84002,
%T A341032 131087,156817,174755,182106,220974,293930,371307,389130,394290,
%U A341032 401573,440819,492886,584326,609301,839590,935685,1727207,1775622,1939666,1948705,2235041,2267650
%N A341032 Numbers k such that A124440(k) is a square.
%C A341032 Terms in common with A341031, i.e. numbers such that both A066840(k) and A124440(k) are squares, include 1, 2, 10, 17, and 25090.
%H A341032 Daniel Suteu, <a href="/A341032/b341032.txt">Table of n, a(n) for n = 1..100</a>
%e A341032 a(4) = 17 is a term because A124440(17) = 100 = 10^2.
%p A341032 N:= 40000: # for terms <= N
%p A341032 G:= add(numtheory:-mobius(n)*n*x^(2*n)/((1-x^n)*(1-x^(2*n))^2), n=1..N/2):
%p A341032 S:= series(G, x, N+1):
%p A341032 A66840:= [seq(coeff(S, x, j), j=1..N)]:
%p A341032 f:= proc(n) n*numtheory:-phi(n)/2 - A66840[n] end proc:
%p A341032 f(1):= 1: f(2):= 1:
%p A341032 select(t -> issqr(f(t)), [$1..N]);
%Y A341032 Cf. A066840, A122440, A341031.
%K A341032 nonn
%O A341032 1,2
%A A341032 _J. M. Bergot_ and _Robert Israel_, Feb 03 2021
%E A341032 More terms from _Daniel Suteu_, Feb 03 2021