login
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
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)
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
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