A373844 Triangle read by rows: T(n,k) = A276086(1 + A002110(n) + A002110(k)), 1 <= k <= n, where A276086 is the primorial base exp-function.

18, 30, 50, 42, 70, 98, 66, 110, 154, 242, 78, 130, 182, 286, 338, 102, 170, 238, 374, 442, 578, 114, 190, 266, 418, 494, 646, 722, 138, 230, 322, 506, 598, 782, 874, 1058, 174, 290, 406, 638, 754, 986, 1102, 1334, 1682, 186, 310, 434, 682, 806, 1054, 1178, 1426, 1798, 1922, 222, 370, 518, 814, 962, 1258, 1406, 1702, 2146, 2294, 2738

Offset

1,1

Comments

Triangle giving all products of three primes, of which one is even (2) and two are odd (not necessarily distinct), so that the product is of the form 4m+2.

The only terms such that T(n, k) > A373845(n, k) > 1 are 30, 42, 110 at positions T(2,1), T(3,1), T(4,2), and the corresponding terms in A373845 are 6, 14, 38.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle

Formula

For n, k >= 1, T(n, k) = A276086(1+A370121(n, k)).

For n, k >= 1, T(n, k) = 2*A087112(n+1, k+1).

Example

Triangle begins as:
   18,
   30,  50,
   42,  70,  98,
   66, 110, 154, 242,
   78, 130, 182, 286, 338,
  102, 170, 238, 374, 442,  578,
  114, 190, 266, 418, 494,  646,  722,
  138, 230, 322, 506, 598,  782,  874, 1058,
  174, 290, 406, 638, 754,  986, 1102, 1334, 1682,
  186, 310, 434, 682, 806, 1054, 1178, 1426, 1798, 1922,
  222, 370, 518, 814, 962, 1258, 1406, 1702, 2146, 2294, 2738,
etc.

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A373844(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2, x=A002110(1+n - binomial(c + 1, 2))); A276086(1+(A002110(1+c)+x)); };

Crossrefs

Cf. A002110, A276086, A370121, A373845.

Cf. also A087112, A369979, A373848.

Sequence in context: A161164 A092357 A141115 * A039320 A043143 A043923

Adjacent sequences: A373841 A373842 A373843 * A373845 A373846 A373847

Keyword

nonn,easy,tabl

Author

Antti Karttunen, Jun 21 2024

Status

approved