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A087112
Triangle in which the n-th row contains n distinct semiprimes not listed previously with all prime factors from among the first n primes.
31
4, 6, 9, 10, 15, 25, 14, 21, 35, 49, 22, 33, 55, 77, 121, 26, 39, 65, 91, 143, 169, 34, 51, 85, 119, 187, 221, 289, 38, 57, 95, 133, 209, 247, 323, 361, 46, 69, 115, 161, 253, 299, 391, 437, 529, 58, 87, 145, 203, 319, 377, 493, 551, 667, 841, 62, 93, 155, 217, 341, 403, 527, 589, 713, 899, 961
OFFSET
1,1
COMMENTS
Terms through row n, sorted, will provide terms forA077553through row n*(n+1)/2.
LINKS
FORMULA
The n-th row consists of n terms, prime(n)*prime(i), i=1..n.
T(n, k) =A000040(n) *A000040(k).
For n >= 2, a(n) =A276086(A370121(n-1)). -Antti Karttunen,Feb 29 2024
EXAMPLE
Triangle begins:
4;
6, 9;
10, 15, 25;
14, 21, 35, 49;
22, 33, 55, 77, 121;
26, 39, 65, 91, 143, 169;
MAPLE
T:= (n, k) -> ithprime(n) * ithprime(k):
seq(print(seq(T(n, k), k = 1..n)), n = 1..11); #Peter Luschny,Jun 25 2024
MATHEMATICA
Table[ Prime[j]*Prime[k], {j, 11}, {k, j}] // Flatten (*Robert G. Wilson v,Feb 06 2017 *)
PROG
(Haskell)
a087112 n k = a087112_tabl!! (n-1)!! (k-1)
a087112_row n = map (* last ps) ps where ps = take n a000040_list
a087112_tabl = map a087112_row [1..]
--Reinhard Zumkeller,Nov 25 2012
(PARI)A087112(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2); (prime(1+c) * prime(1+(n-binomial(1+c, 2)))); }; \\Antti Karttunen,Feb 29 2024
CROSSREFS
Cf.A100484(left edge),A001248(right edge),A143215(row sums),A219603(central terms of odd-indexed rows);A000040,A065342.
KEYWORD
nonn,tabl
AUTHOR
Ray Chandler,Aug 21 2003
STATUS
approved