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A370134 Triangle read by rows: T(n,k) = A002110(n) + A002110(k), 1 <= k <= n; sums of two primorials > 1, not necessarily distinct.

%I A370134 #12 Mar 09 2024 01:44:40
%S A370134 4,8,12,32,36,60,212,216,240,420,2312,2316,2340,2520,4620,30032,30036,
%T A370134 30060,30240,32340,60060,510512,510516,510540,510720,512820,540540,
%U A370134 1021020,9699692,9699696,9699720,9699900,9702000,9729720,10210200,19399380,223092872,223092876,223092900,223093080,223095180,223122900,223603380
%N A370134 Triangle read by rows: T(n,k) = A002110(n) + A002110(k), 1 <= k <= n; sums of two primorials > 1, not necessarily distinct.
%H A370134 Antti Karttunen, <a href="/A370134/b370134.txt">Table of n, a(n) for n = 1..5050; the first 100 rows of triangle, flattened</a>
%H A370134 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A370134 For n >= 1, A276150(a(n)) = 2.
%e A370134 Triangle begins as:
%e A370134         4;
%e A370134         8,      12;
%e A370134        32,      36,      60;
%e A370134       212,     216,     240,     420;
%e A370134      2312,    2316,    2340,    2520,    4620;
%e A370134     30032,   30036,   30060,   30240,   32340,   60060;
%e A370134    510512,  510516,  510540,  510720,  512820,  540540, 1021020;
%e A370134   9699692, 9699696, 9699720, 9699900, 9702000, 9729720, 10210200, 19399380;
%t A370134 nn = 20; MapIndexed[Set[P[First[#2] - 1], #1] &, FoldList[Times, 1, Prime@ Range[nn + 1]]]; Table[(P[n] + P[k]), {n, nn}, {k, n}] (* _Michael De Vlieger_, Mar 08 2024 *)
%o A370134 (PARI)
%o A370134 A002110(n) = prod(i=1,n,prime(i));
%o A370134 A370134(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2); (A002110(1+c) + A002110(1+n - binomial(c + 1, 2))); };
%Y A370134 A370121 without its leftmost column. Subsequence of  A370132.
%Y A370134 Cf. A002110, A049345, A087112, A276150, A370135.
%Y A370134 Cf. A088860 (right edge).
%K A370134 nonn,tabl
%O A370134 1,1
%A A370134 _Antti Karttunen_, Mar 07 2024