A090494 Product_{j=1..n} Product_{k=1..n} lcm(j,k).
1, 1, 8, 7776, 1146617856, 1289945088000000000, 46798828032806092800000000000, 2350577043461005964030008507760640000000000000, 8206262459636402163263383676462776103575725539328000000000000000, 2746781358330240881921653545637784861521126603512175621574459373964492800000000000000000
Offset: 0
Keywords
Programs
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Maple
f := n->mul(mul(lcm(j,k),k=1..n),j=1..n);
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