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Search: id:A090494
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| A090494 |
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Product_{j=1..n} Product_{k=1..n} lcm(j,k). |
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+0
2
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| 1, 1, 8, 7776, 1146617856, 1289945088000000000, 46798828032806092800000000000, 2350577043461005964030008507760640000000000000, 8206262459636402163263383676462776103575725539328000000000000000, 27467813583302408819216535456377848615211266035121756215744593739644928000000000\ 00000000
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OFFSET
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0,3
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FORMULA
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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 (pbala(AT)toucansurf.com), Apr 23 2007
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MAPLE
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f := n->mul(mul(lcm(j, k), k=1..n), j=1..n);
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CROSSREFS
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Cf. A018806, A090494.
Cf. A092143, A092287, A129365, A129454.
Sequence in context: A079189 A114133 A115442 this_sequence A079656 A114773 A057107
Adjacent sequences: A090491 A090492 A090493 this_sequence A090495 A090496 A090497
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2004
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