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Symmetric square array read by antidiagonals: T(n,k) = p(n)*p(k)-p(n*k), where p(i) = prime(i), for n>=1, k>=1.
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%I #18 Sep 11 2019 12:28:44

%S 2,3,3,5,2,5,7,2,2,7,11,2,2,2,11,13,4,-2,-2,4,13,17,2,8,-4,8,2,17,19,

%T 8,4,6,6,4,8,19,23,4,12,2,24,2,12,4,23,29,8,6,12,30,30,12,6,8,29,31,

%U 16,12,2,38,18,38,2,12,16,31,37,14,32,10,36,40,40,36,10,32,14,37,41,22,18,30,56,24,62,24,56,30,18,22,41

%N Symmetric square array read by antidiagonals: T(n,k) = p(n)*p(k)-p(n*k), where p(i) = prime(i), for n>=1, k>=1.

%C Mitrinovic et al. appear to assert that T(n,k) > 0 for all n,k, but presumably they should have said T(n,k) > 0 for all n+k >= 8.

%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.18, p. 247.

%H Seiichi Manyama, <a href="/A324799/b324799.txt">Antidiagonals n = 1..140, flattened</a>

%H H. Ishikawa, <a href="https://www.jstage.jst.go.jp/article/tmj1911/32/0/32_0_328/_article/-char/en">Über die Verteilung der Primzahlen</a>, Sci. Rep. Tokyo Univ. Lit. Sci. Sect. A, 2 (1934), 27-40.

%e The first few antidiagonals are:

%e 2,

%e 3, 3,

%e 5, 2, 5,

%e 7, 2, 2, 7,

%e 11, 2, 2, 2, 11,

%e 13, 4, -2, -2, 4, 13,

%e 17, 2, 8, -4, 8, 2, 17,

%e 19, 8, 4, 6, 6, 4, 8, 19,

%e 23, 4, 12, 2, 24, 2, 12, 4, 23,

%e 29, 8, 6, 12, 30, 30, 12, 6, 8, 29,

%e 31, 16, 12, 2, 38, 18, 38, 2, 12, 16, 31,

%e ...

%Y Main diagonal of the square array is A123914.

%K sign,tabl,look

%O 1,1

%A _N. J. A. Sloane_, Sep 11 2019