A286947 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).

1, 3, 2, 15, 20, 24, 105, 140, 84, 90, 1155, 770, 924, 1980, 2100, 15015, 10010, 24024, 4290, 13650, 23100, 255255, 340340, 204204, 364650, 464100, 353430, 60060, 4849845, 6466460, 5819814, 1385670, 3527160, 5969040, 570570, 510510, 111546435, 74364290, 44618574, 127481640, 81124680, 102965940, 39369330, 58708650, 29099070

Offset: 1

Author

David A. Corneth, May 17 2017

Keywords

• nonn
• tabl

Comments

1 + the Rowsum of row(n) gives a multiple of A002110(n).

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.

T(n,k) is a multiple of A258566(n,k). - Peter Munn, Jan 13 2018

Examples

			Row(1): [1]
Row(2): [3, 2]
Row(3): [15, 20, 24]
Row(4): [105, 140, 84, 90]
Row(5): [1155, 770, 924, 1980, 2100]
Row(6): [15015, 10010, 24024, 4290, 13650, 23100]
Row(7): [255255, 340340, 204204, 364650, 464100, 353430, 60060]
Row(8): [4849845, 6466460, 5819814, 1385670, 3527160, 5969040, 570570, 510510]
Row(4) = [105, 140, 84, 90].
Adding 1 to T(4, 1) gives [106,140,84,90], all elements divisible by prime(1) = 2.
Adding 1 to T(4, 2) gives [105,141,84,90], all elements divisible by prime(2) = 3.
Adding 1 to T(4, 3) gives [105,140,85,90], all elements divisible by prime(3) = 5.
Adding 1 to T(4, 4) gives [105,140,84,91], all elements divisible by prime(4) = 7.
The sum of elements in row 3 is 15 + 20 + 24 = 59. 59 + 1 = 60, a multiple of A002110(3) = 30.
		

Crossrefs

Cf. A002110, A075306, A258566, A286930.

Programs

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

Formula

T(n, 1) = A002110(n) / 2.

For n >= 2, T(n,n) = A075306(n-1) - 1. - Peter Munn, Jan 13 2018

Extensions

Name corrected by Peter Munn, Jan 12 2018