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A324799 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.

%I A324799 #18 Sep 11 2019 12:28:44
%S A324799 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 A324799 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 A324799 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 A324799 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 A324799 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 A324799 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.18, p. 247.
%H A324799 Seiichi Manyama, <a href="/A324799/b324799.txt">Antidiagonals n = 1..140, flattened</a>
%H A324799 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 A324799 The first few antidiagonals are:
%e A324799 2,
%e A324799 3, 3,
%e A324799 5, 2, 5,
%e A324799 7, 2, 2, 7,
%e A324799 11, 2, 2, 2, 11,
%e A324799 13, 4, -2, -2, 4, 13,
%e A324799 17, 2, 8, -4, 8, 2, 17,
%e A324799 19, 8, 4, 6, 6, 4, 8, 19,
%e A324799 23, 4, 12, 2, 24, 2, 12, 4, 23,
%e A324799 29, 8, 6, 12, 30, 30, 12, 6, 8, 29,
%e A324799 31, 16, 12, 2, 38, 18, 38, 2, 12, 16, 31,
%e A324799 ...
%Y A324799 Main diagonal of the square array is A123914.
%K A324799 sign,tabl,look
%O A324799 1,1
%A A324799 _N. J. A. Sloane_, Sep 11 2019