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Amiram Eldar, <a href="/A333913/b333913.txt">Table of n, a(n) for n = 1..10000</a>

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1 is not a term since lambda(1) = 1 = 0^2 + 0^2 + 1 ^2 is the sum of 3 squares.

Cf. A002322, A004215, A173694, A272405, A333912.

Paul Pollack, <a href="https://www.emis.de/journals/INTEGERS/papers/l13/l13.Abstract.html">Values of the Euler and Carmichael functions which are sums of three squares</a>, Integers, Vol. 11 (2011), pp. 145-161, <a href="http://pollack.uga.edu/phi3squares.pdf">alternative link</a>.

allocated for Amiram EldarNumbers k such that lambda(k) is not the sum of 3 squares, where lambda is the Carmichael lambda function (A002322).

29, 58, 61, 87, 113, 116, 122, 143, 145, 155, 157, 169, 174, 175, 183, 225, 226, 232, 235, 241, 244, 286, 290, 305, 310, 314, 317, 325, 338, 339, 348, 349, 350, 366, 371, 385, 395, 403, 427, 429, 435, 449, 450, 452, 464, 465, 470, 471, 477, 482, 488, 493, 495

1,1

Pollack (2011) proved that this sequence has a lower and an upper asymptotic densities, and conjectured that they do not coincide.

Paul Pollack, <a href="https://www.emis.de/journals/INTEGERS/papers/l13/l13.Abstract.html">Values of the Euler and Carmichael functions which are sums of three squares</a>, Integers, Vol. 11 (2011), pp. 145-161, <a href="http://pollack.uga.edu/phi3squares.pdf">alternative link</a>.

1 is not a term since lambda(1) = 1 = 0^2 + 0^2 + 1 is the sum of 3 squares.

29 is a term since lambda(29) = 28 is not the sum of 3 squares.

Select[Range[500], SquaresR[3, CarmichaelLambda[#]] == 0 &]

Cf. A002322, A004215, A173694, A333912.

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Amiram Eldar, Apr 09 2020

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