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A369979 Three-dimensional array giving all products of three (not necessarily distinct) odd primes.

%I A369979 #12 Mar 09 2024 13:03:25
%S A369979 27,45,75,125,63,105,175,147,245,343,99,165,275,231,385,539,363,605,
%T A369979 847,1331,117,195,325,273,455,637,429,715,1001,1573,507,845,1183,1859,
%U A369979 2197,153,255,425,357,595,833,561,935,1309,2057,663,1105,1547,2431,2873,867,1445,2023,3179,3757,4913,171,285,475,399,665,931
%N A369979 Three-dimensional array giving all products of three (not necessarily distinct) odd primes.
%C A369979 For n > 20, a(n) < A370138(n).
%H A369979 Antti Karttunen, <a href="/A369979/b369979.txt">Table of n, a(n) for n = 1..15180</a>
%F A369979 For n > 1, a(n) = A276086(A370137(n)).
%e A369979 Table T(x,y,z) = A065091(x) * A065091(y) * A065091(z), x >= y >= z >= 1, is read by lexicographical ordering of weakly decreasing triplets (x,y,z):
%e A369979 (1, 1, 1) -> 3*3*3 = 27;
%e A369979 (2, 1, 1) -> 5*3*3 = 45, (2, 2, 1) -> 5*5*3 = 75, (2, 2, 2) -> 5*5*5 = 125;
%e A369979 (3, 1, 1) -> 7*3*3 = 63, (3, 2, 1) -> 7*5*3 = 105, (3, 2, 2) -> 7*5*5 = 175, (3, 3, 1) -> 7*7*3 = 147, (3, 3, 2) -> 7*7*5 = 245, (3, 3, 3) -> 7*7*7 = 343.
%t A369979 Table[Prime[i]*Prime[j]*Prime[k], {i, 2, 8}, {j, 2, i}, {k, 2, j}] // Flatten (* _Michael De Vlieger_, Mar 09 2024 *)
%o A369979 (PARI)
%o A369979 up_to = 15180;
%o A369979 A369979list(up_to) = { my(v = vector(up_to), i=0); for(x=1,oo, for(y=1,x, for(z=1,y, i++; if(i > up_to, return(v)); v[i] = prime(1+x)*prime(1+y)*prime(1+z)))); (v); };
%o A369979 v369979 = A369979list(up_to);
%o A369979 A369979(n) = v369979[n];
%Y A369979 Cf. A000292, A046316 (same sequence sorted into ascending order), A065091, A276086, A370137, A370138.
%Y A369979 Cf. also A087112.
%K A369979 nonn,tabf
%O A369979 1,1
%A A369979 _Antti Karttunen_, Mar 09 2024