A235507 Harshad numbers which when divided by sum of their digits, give a quotient which is a Harshad number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 108, 120, 162, 180, 200, 210, 216, 240, 243, 270, 300, 324, 360, 378, 400, 405, 420, 432, 450, 480, 486, 500, 540, 600, 630, 648, 700, 720

Offset

1,2

Comments

These numbers are also called MHN-2 or Multiple Harshad Numbers-2.

Links

Ray Chandler, Table of n, a(n) for n = 1..10796 (all a(n) <= 10^6)

Wikipedia, Harshad Number

Example

486 is a MHN as it is divisible by the sum of its digits i.e. 18. The quotient obtained, 27, is also divisible by the sum of its digits, i.e. 9.

Mathematica

mhnQ[n_]:=Module[{s=Total[IntegerDigits[n]]}, Divisible[n, s]&&Divisible[ n/s, Total[IntegerDigits[n/s]]]]; Select[Range[800], mhnQ] (* Harvey P. Dale, Sep 02 2017 *)

Crossrefs

Cf. A005349, A235697.

Sequence in context: A285829 A225780 A225782 * A235697 A085135 A085133

Adjacent sequences: A235504 A235505 A235506 * A235508 A235509 A235510

Keyword

nonn,base

Author

Mihir Mathur, Jan 14 2014

Status

approved