A090494 Product_{j=1..n} Product_{k=1..n} lcm(j,k).

1, 1, 8, 7776, 1146617856, 1289945088000000000, 46798828032806092800000000000, 2350577043461005964030008507760640000000000000, 8206262459636402163263383676462776103575725539328000000000000000, 2746781358330240881921653545637784861521126603512175621574459373964492800000000000000000

Offset

0,3

Links

Table of n, a(n) for n=0..9.

Formula

Let p be a prime and let ordp(n,p) denote the exponent of the largest power of p which divides n. For example, ordp(48,2)=4 since 48 = 3*(2^4). Then the prime factorization of a(n) appears to be given by the formula ordp(a(n),p)= sum_{k >= 1} [(2*(p^k)-1)*floor((n/(p^k)))^2] + 2*sum_{k >= 1} [floor(n/(p^k))*mod(n,p^k)], for each prime p. See the comments sections of A092143, A092287, A129365 and A129454 for similar conjectural prime factorizations. - Peter Bala, Apr 23 2007

Maple

f := n->mul(mul(lcm(j, k), k=1..n), j=1..n);

Crossrefs

Cf. A018806.

Cf. A092143, A092287, A129365, A129454.

Sequence in context: A278854 A115442 A216936 * A079656 A114773 A057107

Adjacent sequences: A090491 A090492 A090493 * A090495 A090496 A090497

Keyword

nonn

Author

N. J. A. Sloane, Feb 03 2004

Status

approved