A085444 Numbers divisible by twice the sum of the products of each of their digits.

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

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 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