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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
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 (list; table; graph; refs; listen; history; text; internal format)
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: A223523 A133932 A111999 * A190961 A126323 A292123

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

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Last modified October 16 18:38 EDT 2019. Contains 328102 sequences. (Running on oeis4.)