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A085444 Numbers evenly divisible by twice the sum of the products of each of their digits. 3
10, 50, 100, 162, 200, 324, 392, 500, 512, 648, 810, 1000, 1120, 1134, 1296, 1400, 1620, 1944, 2000, 2106, 2300, 2430, 2592, 2704, 2800, 3200, 3240, 3402, 3920, 4000, 4050, 4100, 4212, 4536, 4600, 5000, 5022, 5120, 5184, 5632, 5832, 6050, 6400, 6480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Take a number n, create a table with d columns and rows where d=number of digits of n. Each column corresponds to a digit of n and each row to a digit of n. In each cell, multiply the two digits of n represented by that row and column. Add up the sums of all of the rows and all of the columns to get a new number m which divides evenly into n.

"The sum of the products of each of [the] digits" is just the square of the sum of the digits. - Franklin T. Adams-Watters, Jul 17 2006

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

EXAMPLE

512 / 2*((5*5)+(5*1)+(5*2)+(1*5)+(1*1)+(1*2)+(2*5)+(2*1)+(2*2)) = 4

MATHEMATICA

ed2Q[n_]:=Module[{idn=IntegerDigits[n]}, Divisible[n, 2Total[ Flatten[ Table[ idn* idn[[i]], {i, Length[idn]}]]]]]; Select[Range[7000], ed2Q] (* Harvey P. Dale, Dec 28 2016 *)

CROSSREFS

Cf. A085445, A085446.

Sequence in context: A243226 A283237 A036786 * A102915 A153780 A196507

Adjacent sequences:  A085441 A085442 A085443 * A085445 A085446 A085447

KEYWORD

base,nonn

AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jun 30 2003

STATUS

approved

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Last modified August 21 13:36 EDT 2017. Contains 290890 sequences.