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A370135 Triangle read by rows: T(n,k) = (A002110(n) + A002110(k)) / A002110(k), 1 <= k <= n.

%I A370135 #13 Mar 09 2024 01:44:22
%S A370135 2,4,2,16,6,2,106,36,8,2,1156,386,78,12,2,15016,5006,1002,144,14,2,
%T A370135 255256,85086,17018,2432,222,18,2,4849846,1616616,323324,46190,4200,
%U A370135 324,20,2,111546436,37182146,7436430,1062348,96578,7430,438,24,2,3234846616,1078282206,215656442,30808064,2800734,215442,12674,668,30,2
%N A370135 Triangle read by rows: T(n,k) = (A002110(n) + A002110(k)) / A002110(k), 1 <= k <= n.
%H A370135 Antti Karttunen, <a href="/A370135/b370135.txt">Table of n, a(n) for n = 1..5050; the first 100 rows of triangle, flattened</a>
%H A370135 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A370135 a(n) = A370134(n) / A002110(A002260(n)).
%e A370135 Triangle begins as:
%e A370135           2;
%e A370135           4,        2;
%e A370135          16,        6,       2;
%e A370135         106,       36,       8,       2;
%e A370135        1156,      386,      78,      12,     2;
%e A370135       15016,     5006,    1002,     144,    14,    2;
%e A370135      255256,    85086,   17018,    2432,   222,   18,   2;
%e A370135     4849846,  1616616,  323324,   46190,  4200,  324,  20,  2;
%e A370135   111546436, 37182146, 7436430, 1062348, 96578, 7430, 438, 24, 2;
%t A370135 nn = 20; MapIndexed[Set[P[First[#2] - 1], #1] &, FoldList[Times, 1, Prime@ Range[nn + 1]]]; Table[(P[n] + P[k])/P[k], {n, nn}, {k, n}] (* _Michael De Vlieger_, Mar 08 2024 *)
%o A370135 (PARI)
%o A370135 A002110(n) = prod(i=1,n,prime(i));
%o A370135 A370135(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2, x=A002110(1+n - binomial(c + 1, 2))); ((A002110(1+c)+x)/x); };
%Y A370135 Cf. A002110, A002260, A370134, A370136 (arithmetic derivatives).
%K A370135 nonn,tabl
%O A370135 1,1
%A A370135 _Antti Karttunen_, Mar 07 2024