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

1, 2, 10, 17, 469, 646, 1542, 1601, 24939, 25090, 43690, 50925, 77577, 84002, 131087, 156817, 174755, 182106, 220974, 293930, 371307, 389130, 394290, 401573, 440819, 492886, 584326, 609301, 839590, 935685, 1727207, 1775622, 1939666, 1948705, 2235041, 2267650

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 03 2021

Keywords

• nonn

Comments

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.

Examples

			a(4) = 17 is a term because A124440(17) = 100 = 10^2.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A066840, A122440, A341031.

Programs

Maple

N:= 40000: # for terms <= N
G:= add(numtheory:-mobius(n)*n*x^(2*n)/((1-x^n)*(1-x^(2*n))^2), n=1..N/2):
S:= series(G, x, N+1):
A66840:= [seq(coeff(S, x, j), j=1..N)]:
f:= proc(n) n*numtheory:-phi(n)/2 - A66840[n] end proc:
f(1):= 1: f(2):= 1:
select(t -> issqr(f(t)), [$1..N]);

Extensions

More terms from Daniel Suteu, Feb 03 2021