A141091 Integral quotients of products of consecutive composites divided by their sums: sums (divisors).

4, 27, 63, 112, 175, 224, 250, 400, 847, 896, 2368, 2448, 2695, 3596, 4300, 4624, 4961, 5076, 5546, 6032, 6156, 6664, 8750, 9048, 9200, 9976, 10295, 11620, 12312, 13572, 14697, 15872, 16275, 18139, 18352, 23572, 24304, 25544, 26814, 27072, 29986

Offset: 1

Author

Enoch Haga, Jun 01 2008

Keywords

• easy
• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A196415, A141089, A141090, A141092.

Compare with A140761, A159578, A140763, A116536.

Programs

Mathematica

comp = Select[Range[500], CompositeQ]; sum = Accumulate[comp]; sum[[Position[ Rest@FoldList[Times, 1, comp]/sum, ?IntegerQ] // Flatten]] (* _Amiram Eldar, Jan 12 2020 *)

Formula

Find the products and sums of consecutive composites. When the products divided by the sums produce integral quotients, add terms to sequence.

Extensions

a(37) corrected by Amiram Eldar, Jan 12 2020