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A266743 Irregular triangle T(n,k) read by rows: see Comments for definition. 3
1, 1, 1, 2, 3, 1, 1, 2, 1, 6, 15, 10, 1, 2, 6, 5, 1, 12, 42, 42, 14, 1, 3, 12, 14, 7, 1, 10, 45, 60, 42, 10, 1, 2, 10, 15, 14, 5, 1, 12, 66, 110, 132, 66, 22, 1, 2, 12, 22, 33, 22, 11, 1, 420, 2730, 5460, 10010, 8580, 6006, 910, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Let p_i denote the i-th prime, let pi(n) = A000720(n), and let N! = Prod_{i = 1..pi(N)} (p_i)^U(N,i) be the prime factorization of N!, where U(N,i) = A115627(N,i).

Let V(n,i) = floor(n/(prime(i)-1)) = A266742(n,i).

The present triangle is defined by T(n,k) =

Prod_i (p_i)^V(n,i) / ( Prod_j (p_j)^V(k,j) * Prod_r (p_r)^U(n-k+1,r) ).

LINKS

Table of n, a(n) for n=1..61.

H. T. Davis, Tables of the Mathematical Functions, Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX. [Annotated scan of pages 204-208 of Volume 2.] See Table 3 on page 207.

EXAMPLE

Triangle begins:

1,

1,1,

2,3,1,

1,2,1,

6,15,10,1,

2,6,5,1,

12,42,42,14,1,

3,12,14,7,1,

10,45,60,42,10,1,

2,10,15,14,5,1,

12,66,110,132,66,22,1,

2,12,22,33,22,11,1,

420,2730,5460,10010,8580,6006,910,1,

...

CROSSREFS

Cf. A000720, A002443, A002444, A115627, A266742.

Sequence in context: A055444 A102383 A070913 * A284050 A114280 A123564

Adjacent sequences:  A266740 A266741 A266742 * A266744 A266745 A266746

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Jan 08 2016

STATUS

approved

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Last modified February 16 18:53 EST 2019. Contains 320165 sequences. (Running on oeis4.)