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

1,1

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A196415, A141089, A141090, A141092.

Compare with A140761, A159578, A140763, A116536.

Sequence in context: A033663 A218629 A190403 * A349200 A078111 A186882

Adjacent sequences: A141088 A141089 A141090 * A141092 A141093 A141094

Keyword

easy,nonn

Author

Enoch Haga, Jun 01 2008

Extensions

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

Status

approved