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%I #17 Jan 20 2018 09:16:39
%S 1,3,2,15,20,24,105,140,84,90,1155,770,924,1980,2100,15015,10010,
%T 24024,4290,13650,23100,255255,340340,204204,364650,464100,353430,
%U 60060,4849845,6466460,5819814,1385670,3527160,5969040,570570,510510,111546435,74364290,44618574,127481640,81124680,102965940,39369330,58708650,29099070
%N Triangle read by rows in which row(n) = {T(n, k)} is the lexicographically earliest list of n numbers such that adding 1 to some T(n, k) gives a row of numbers each divisible by prime(k).
%C 1 + the Rowsum of row(n) gives a multiple of A002110(n).
%C c = Product_{i=1..n} prime(i)^T(n, i) is the least term such that prime(i) * c is a prime(i)-th power. First such terms are 2, 72, 6810125783203125000000000000000, ... which relates this sequence to A286930.
%C T(n,k) is a multiple of A258566(n,k). - _Peter Munn_, Jan 13 2018
%F T(n, 1) = A002110(n) / 2.
%F For n >= 2, T(n,n) = A075306(n-1) - 1. - _Peter Munn_, Jan 13 2018
%e Row(1): [1]
%e Row(2): [3, 2]
%e Row(3): [15, 20, 24]
%e Row(4): [105, 140, 84, 90]
%e Row(5): [1155, 770, 924, 1980, 2100]
%e Row(6): [15015, 10010, 24024, 4290, 13650, 23100]
%e Row(7): [255255, 340340, 204204, 364650, 464100, 353430, 60060]
%e Row(8): [4849845, 6466460, 5819814, 1385670, 3527160, 5969040, 570570, 510510]
%e Row(4) = [105, 140, 84, 90].
%e Adding 1 to T(4, 1) gives [106,140,84,90], all elements divisible by prime(1) = 2.
%e Adding 1 to T(4, 2) gives [105,141,84,90], all elements divisible by prime(2) = 3.
%e Adding 1 to T(4, 3) gives [105,140,85,90], all elements divisible by prime(3) = 5.
%e Adding 1 to T(4, 4) gives [105,140,84,91], all elements divisible by prime(4) = 7.
%e The sum of elements in row 3 is 15 + 20 + 24 = 59. 59 + 1 = 60, a multiple of A002110(3) = 30.
%o (PARI) row(n) = my(pr=primes(n), p = prod(i=1, #pr, pr[i]), res=vector(n, i, lift(chinese(Mod(-1, pr[i]), Mod(0, p/pr[i]))))); res
%Y Cf. A002110, A075306, A258566, A286930.
%K nonn,tabl
%O 1,2
%A _David A. Corneth_, May 17 2017
%E Name corrected by _Peter Munn_, Jan 12 2018
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