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Numbers that are the products of 2 or more consecutive integers.
+10
17
0, 2, 6, 12, 20, 24, 30, 42, 56, 60, 72, 90, 110, 120, 132, 156, 182, 210, 240, 272, 306, 336, 342, 360, 380, 420, 462, 504, 506, 552, 600, 650, 702, 720, 756, 812, 840, 870, 930, 990, 992, 1056, 1122, 1190, 1260, 1320, 1332, 1406, 1482, 1560, 1640, 1680
Numbers having more than one representation as the product of consecutive integers.
+10
3
6, 24, 120, 210, 720, 5040, 40320, 175560, 362880, 3628800, 17297280, 19958400, 39916800, 259459200, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 20274183401472000, 121645100408832000
COMMENTS
All the factorials occur because we allow products to start with 1. See A064224 for a more restrictive case.
CROSSREFS
Cf. A064224, A003015 (numbers occurring 5 or more times in Pascal's triangle).
Highly composite numbers that are the product of consecutive integers.
+10
3
2, 6, 12, 24, 60, 120, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 15120, 20160, 50400, 55440, 166320, 332640, 665280, 2162160, 3603600, 4324320, 8648640, 17297280, 32432400, 43243200
Numbers having multiple representations as the product of non-overlapping ranges of consecutive numbers.
+10
2
210, 720, 175560, 17297280
COMMENTS
A subsequence of A064224. This sequence gives solutions P to the equation P = (x+1)...(x+m) = (y+1)...(y+n) with x>0, y>0 and x+m < y+1. So far, no numbers P with more than two representations have been discovered. Note that the only the lowest range of consecutive numbers (x+1 to x+m) can contain prime numbers; the other ranges are in a gap between consecutive primes. Gaps between the first 45000 primes were searched for additional terms, but none were found.
Numbers that can be written as a product of k consecutive composite numbers and also of k+1 consecutive composite numbers, for some k>1, with no factor used twice.
+10
2
1680, 4320, 120960, 166320, 175560, 215760, 725760, 1080647568000
Numbers having more than one representation as the product of at least two consecutive odd integers > 1.
+10
0
135135, 2110886623587616875, 118810132577324221759073444371080321140625, 262182986027006205192949807157375529898104505103011391412633845449072265625
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