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

1,2

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

Links

Table of n, a(n) for n=1..45.

Formula

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

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

Example

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.

Prog

(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

Crossrefs

Cf. A002110, A075306, A258566, A286930.

Sequence in context: A357613 A133932 A111999 * A334559 A190961 A346059

Adjacent sequences: A286944 A286945 A286946 * A286948 A286949 A286950

Keyword

nonn,tabl

Author

David A. Corneth, May 17 2017

Extensions

Name corrected by Peter Munn, Jan 12 2018

Status

approved