A342876 -id:A342876 - cp's OEIS frontend

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.

1680, 4320, 120960, 166320, 175560, 215760, 725760, 1080647568000

Offset: 1

Manuel Valdivia, Apr 16 2010, Apr 18 2010

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)

			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)

Cf. A002808, A064224, A163263, A342876.

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.

Definition edited by N. J. A. Sloane, Apr 18 2010

Keyword:base removed by R. J. Mathar, Apr 24 2010

A343459 Numbers that can be expressed both as the product of two consecutive composite numbers and as the product of three consecutive composite numbers.

Original entry on oeis.org

1680, 175560, 215760

Offset: 1

Jon E. Schoenfield, Apr 15 2021

Sequence contains only three terms.

			    1680 =  40 *  42 = 10 * 12 * 14.
  175560 = 418 * 420 = 55 * 56 * 57.
  215760 = 464 * 465 = 58 * 60 * 62.

Cf. A342876.

cp's OEIS Frontend

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.

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