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 A175340 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. 2
 1680, 4320, 120960, 166320, 175560, 215760, 725760, 1080647568000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The term 725760 has three representations of 4, 5 and 6 numbers (with overlap). From David A. Corneth, Mar 27 2021, Mar 28 2021: (Start) a(12) > 10^22 if it exists. Let x be the product of k consecutive composite numbers and y be the product of k+1 consecutive composite numbers giving some a(m). This sequence does not allow factors of x and y to overlap. If we do allow such overlaps we get A342876. (End) LINKS Table of n, a(n) for n=1..8. FORMULA Numbers of the form Product_{i=x..x+k} A002808(i) = Product_{i=y..y+k-1} A002808(i), where y > x + k and k > 1. EXAMPLE 1680 = 10*12*14 = 40*42. 4320 = 6*8*9*10 = 15*16*18. 120960 = 8*9*10*12*14 = 16*18*20*21. 166320 = 18*20*21*22 = 54*55*56. 175560 = 55*56*57 = 418*420. 215760 = 58*60*62 = 464*465. 725760 = 12*14*15*16*18 = 27*28*30*32. 1080647568000 = 49*50*51*52*54*55*56 = 98*99*100*102*104*105. From David A. Corneth, Mar 28 2021: (Start) 1814400 = 8*9*10*12*14*15 = 15*16*18*20*21 is not in the sequence as the factor 15 is used more than once. 104613949440000 = 12*14*15*16*18*20*21*22*24*25*26 = 20*21*22*24*25*26*27*28*30*32 is not here because, among others, the factor 20 is used more than once. 115880067072000 = 4*6*8*9*10*12*14*15*16*18*20*21*22 = 8*9*10*12*14*15*16*18*20*21*22*24 is not here because most factors are used more than once. (End) CROSSREFS Cf. A002808, A064224, A163263, A342876. Sequence in context: A179693 A290704 A342876 * A181928 A234439 A060095 Adjacent sequences: A175337 A175338 A175339 * A175341 A175342 A175343 KEYWORD nonn,more AUTHOR Manuel Valdivia, Apr 16 2010, Apr 18 2010 EXTENSIONS Definition edited by N. J. A. Sloane, Apr 18 2010 Keyword:base removed by R. J. Mathar, Apr 24 2010 STATUS approved

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Last modified October 3 16:48 EDT 2023. Contains 365868 sequences. (Running on oeis4.)