A141090 Integral quotients of products of first k consecutive composites divided by their sums: products (dividends).

4, 1728, 2903040, 12541132800, 115880067072000, 69528040243200000, 1807729046323200000, 43295255277764345856000000, 20188846756043686829592191472500736000000000, 989253491046140654650017382152536064000000000

Offset: 1

Author

Enoch Haga, Jun 01 2008

Keywords

• easy
• nonn

Comments

Based on A141092.

Compare with A140761 A159578 A140763 A116536.

Take the first k composite numbers. If their product divided by their sum results in an integer, their product is a term of the sequence. - Harvey P. Dale, Apr 29 2018

Examples

			a(3) = 2903040 because 4*6*8*9*10*12*14 = 2903040 and 4+6+8+9+10+12+14 = 63; 2903040/63 = 46080, integral -- 2903040 is added to the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..93

Crossrefs

Cf. A196415, A141089, A141091, A141092.

Programs

Mathematica

With[{c=Select[Range[100],CompositeQ]},Table[If[IntegerQ[ Times@@Take[ c,n]/Total[ Take[ c,n]]], Times@@ Take[ c,n],0],{n,Length[c]}]]/.(0-> Nothing) (* Harvey P. Dale, Apr 29 2018 *)

Formula

Find the products and sums of first k consecutive composites. When the product divided by the sum produces an integral quotient, add product to sequence.

Extensions

Checked by N. J. A. Sloane, Oct 02 2011

Edited by N. J. A. Sloane, Apr 29 2018