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A096334
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Triangle read by rows: T(n,k) = prime(n)#/prime(k)#, 0<=k<=n.
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5
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1, 2, 1, 6, 3, 1, 30, 15, 5, 1, 210, 105, 35, 7, 1, 2310, 1155, 385, 77, 11, 1, 30030, 15015, 5005, 1001, 143, 13, 1, 510510, 255255, 85085, 17017, 2431, 221, 17, 1, 9699690, 4849845, 1616615, 323323, 46189, 4199, 323, 19, 1, 223092870, 111546435, 37182145, 7436429, 1062347, 96577, 7429, 437, 23, 1
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OFFSET
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0,2
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COMMENTS
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T(n,k) is the (k+1)-th product of (n-k) successive primes (k, n-(k+1) >= 0). - Alois P. Heinz, Jan 21 2022
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
2, 1;
6, 3, 1;
30, 15, 5, 1;
210, 105, 35, 7, 1;
...
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MAPLE
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T:= proc(n, k) option remember;
`if`(n=k, 1, T(n-1, k)*ithprime(n))
end:
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MATHEMATICA
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T[n_, k_] := Times @@ Prime[Range[k + 1, n]];
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PROG
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(PARI) pr(n) = factorback(primes(n)); \\ A002110
row(n) = my(P=pr(n)); vector(n+1, k, P/pr(k-1)); \\ Michel Marcus, Jan 21 2022
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CROSSREFS
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T(n-1+j,n-1) give (j=1-12): A000040, A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127342, A127343, A127344.
Cf. A073485 (distinct values sorted).
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KEYWORD
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AUTHOR
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STATUS
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approved
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