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
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
Programs
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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
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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
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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
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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
Comments