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%I #7 Apr 23 2024 08:28:47
%S 0,1,1,2,0,2,4,8,8,4,4,0,0,0,4,8,24,32,32,24,8,6,8,56,0,56,8,6,16,48,
%T 36,96,96,36,48,16,18,0,108,32,0,32,108,0,18,24,72,128,192,176,176,
%U 192,128,72,24,10,16,0,0,264,0,264,0,0,16,10,32,120,176,288,384,360,360,384,288
%N Array T(m,n) = phi(m^2)*phi(n^2) - phi(m*n)^2 (m,n >= 1), read by antidiagonals.
%C It is known that phi(m^2)*phi(n^2) >= phi(m*n)^2.
%D József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter I, p. 9, section I.2.2.
%e Array begins:
%e m\n | 1 2 3 4 5 6 ...
%e ----+--------------------------------
%e 1 | 0 1 2 4 4 8 ...
%e 2 | 1 0 8 0 24 8 ...
%e 3 | 2 8 0 32 56 36 ...
%e 4 | 4 0 32 0 96 32 ...
%e 5 | 4 24 56 96 0 176 ...
%e 6 | 8 8 36 32 176 0 ...
%e ...
%t T[m_, n_] := EulerPhi[m^2] * EulerPhi[n^2] - EulerPhi[m*n]^2; Table[T[m, n-m+1], {n, 1, 12}, {m, 1, n}] // Flatten (* _Amiram Eldar_, Apr 23 2024 *)
%Y Cf. A000010, A076953, A079548, A079549.
%K nonn,tabl,changed
%O 1,4
%A _N. J. A. Sloane_, Jan 24 2003
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