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A141091 Integral quotients of products of consecutive composites divided by their sums: sums (divisors). 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A078111 A186882 A097792

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

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Last modified October 25 06:05 EDT 2020. Contains 338011 sequences. (Running on oeis4.)