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A373844 Triangle read by rows: T(n,k) = A276086(1 + A002110(n) + A002110(k)), 1 <= k <= n, where A276086 is the primorial base exp-function.

%I A373844 #9 Jun 21 2024 14:18:28
%S A373844 18,30,50,42,70,98,66,110,154,242,78,130,182,286,338,102,170,238,374,
%T A373844 442,578,114,190,266,418,494,646,722,138,230,322,506,598,782,874,1058,
%U A373844 174,290,406,638,754,986,1102,1334,1682,186,310,434,682,806,1054,1178,1426,1798,1922,222,370,518,814,962,1258,1406,1702,2146,2294,2738
%N A373844 Triangle read by rows: T(n,k) = A276086(1 + A002110(n) + A002110(k)), 1 <= k <= n, where A276086 is the primorial base exp-function.
%C A373844 Triangle giving all products of three primes, of which one is even (2) and two are odd (not necessarily distinct), so that the product is of the form 4m+2.
%C A373844 The only terms such that T(n, k) > A373845(n, k) > 1 are 30, 42, 110 at positions T(2,1), T(3,1), T(4,2), and the corresponding terms in A373845 are 6, 14, 38.
%H A373844 Antti Karttunen, <a href="/A373844/b373844.txt">Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle</a>
%F A373844 For n, k >= 1, T(n, k) = A276086(1+A370121(n, k)).
%F A373844 For n, k >= 1, T(n, k) = 2*A087112(n+1, k+1).
%e A373844 Triangle begins as:
%e A373844    18,
%e A373844    30,  50,
%e A373844    42,  70,  98,
%e A373844    66, 110, 154, 242,
%e A373844    78, 130, 182, 286, 338,
%e A373844   102, 170, 238, 374, 442,  578,
%e A373844   114, 190, 266, 418, 494,  646,  722,
%e A373844   138, 230, 322, 506, 598,  782,  874, 1058,
%e A373844   174, 290, 406, 638, 754,  986, 1102, 1334, 1682,
%e A373844   186, 310, 434, 682, 806, 1054, 1178, 1426, 1798, 1922,
%e A373844   222, 370, 518, 814, 962, 1258, 1406, 1702, 2146, 2294, 2738,
%e A373844 etc.
%o A373844 (PARI)
%o A373844 A002110(n) = prod(i=1,n,prime(i));
%o A373844 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A373844 A373844(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2, x=A002110(1+n - binomial(c + 1, 2))); A276086(1+(A002110(1+c)+x)); };
%Y A373844 Cf. A002110, A276086, A370121, A373845.
%Y A373844 Cf. also A087112, A369979, A373848.
%K A373844 nonn,easy,tabl
%O A373844 1,1
%A A373844 _Antti Karttunen_, Jun 21 2024