A228017 Numbers n divisible by the sum of any k-subset of digits of n with k >= 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48

Offset: 1

Author

Derek Orr, Aug 02 2013

Keywords

• nonn
• base
• fini
• full

Comments

No additional terms less than 20000000. - T. D. Noe, Aug 14 2013

Terms > 9 must be even since any pair of digits has an even subset. Since terms must also be zeroless, they cannot be divisible by 5, which means no further terms could have 5 or more digits by the Pigeonhole Principle. Therefore, this sequence is complete. - Charlie Neder, May 31 2019

Examples

			48 is here because 48 is divisible by 4, 8, and 4+8.
		

Crossrefs

Subset of A051004 and of A346535.

Programs

Mathematica

okQ[n_] := Module[{s = Total /@ Rest[Subsets[IntegerDigits[n]]]}, ! MemberQ[s, 0] && And @@ IntegerQ /@ (n/s)]; Select[Range[10000], okQ] (* T. D. Noe, Aug 14 2013 *)