A098012 Triangle read by rows in which the k-th term in row n (n >= 1, k = 1..n) is Product_{i=0..k-1} prime(n-i).

2, 3, 6, 5, 15, 30, 7, 35, 105, 210, 11, 77, 385, 1155, 2310, 13, 143, 1001, 5005, 15015, 30030, 17, 221, 2431, 17017, 85085, 255255, 510510, 19, 323, 4199, 46189, 323323, 1616615, 4849845, 9699690, 23, 437, 7429, 96577, 1062347, 7436429, 37182145, 111546435, 223092870

Offset: 1

Author

Alford Arnold, Sep 09 2004

Keywords

• easy
• nonn
• tabl

Comments

Also, square array A(m,n) in which row m lists all products of m consecutive primes (read by falling antidiagonals). See also A248164. - M. F. Hasler, May 03 2017

Examples

			2
3 3*2
5 5*3 5*3*2
7 7*5 7*5*3 7*5*3*2
Or, as an infinite square array:
     2     3     5     7  ... : row 1 = A000040,
     6    15    35    77  ... : row 2 = A006094,
    30   105   385  1001  ... : row 3 = A046301,
   210  1155  5005 17017  ... : row 4 = A046302,
   ..., with col.1 = A002110, col.2 = A070826, col.3 = A059865\{1}. - _M. F. Hasler_, May 03 2017
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A000040, A002110, A006094, A046301, A046302, A046303.

Cf. A060381 (central terms), A104887, A248147.

Programs

GAP

P:=Filtered([1..200],IsPrime);;
T:=Flat(List([1..9],n->List([1..n],k->Product([0..k-1],i->P[n-i])))); # Muniru A Asiru, Mar 16 2019

Haskell

a098012 n k = a098012_tabl !! (n-1) !! (k-1)
a098012_row n = a098012_tabl !! (n-1)
a098012_tabl = map (scanl1 (*)) a104887_tabl
-- Reinhard Zumkeller, Oct 02 2014

Maple

T:=(n,k)->mul(ithprime(n-i),i=0..k-1): seq(seq(T(n,k),k=1..n),n=1..9); # Muniru A Asiru, Mar 16 2019

Mathematica

Flatten[ Table[ Product[ Prime[i], {i, n, j, -1}], {n, 9}, {j, n, 1, -1}]] (* Robert G. Wilson v, Sep 21 2004 *)

PARI

T098012(n,k)=prod(i=0,k-1,prime(n-i)) \\ "Triangle" variant
A098012(m,n)=prod(i=0,m-1,prime(n+i)) \\ "Square array" variant. - M. F. Hasler, May 03 2017

Formula

n-th row = partial products of row n in A104887. - Reinhard Zumkeller, Oct 02 2014

Extensions

More terms from Robert G. Wilson v, Sep 21 2004