A280355 Numbers that are divisible by the sum of their digits and for which the sum of digits equals the product of digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 132, 312, 4112, 11133, 11313, 11331, 13113, 13131, 13311, 22112, 31113, 31131, 31311, 33111, 111216, 111612, 112116, 116112, 121116, 161112, 211116, 611112, 1111712, 11111232, 11112132, 11112312, 11113212, 11118112, 11121132, 11121312, 11123112, 11131212, 11132112

Offset: 1

Author

Ilya Gutkovskiy, Jan 01 2017

Keywords

• nonn
• base
• easy

Examples

			132 is in the sequence because 1 + 3 + 2 = 1*3*2 = 6 and 6 divides 132.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Harshad Numbers

Crossrefs

Intersection of A005349 and A034710.

Cf. A038186.

Programs

Mathematica

Select[Range[11300000], Divisible[#1, (Plus @@ IntegerDigits[#1])] && (Plus @@ IntegerDigits[#1]) == (Times @@ IntegerDigits[#1]) &]
nQ[n_]:=With[{idn=IntegerDigits[n]},Mod[n,Total[idn]]==0&&Total[idn]==Times@@idn]; Select[Range[112*10^5],nQ] (* Harvey P. Dale, Nov 02 2024 *)

PARI

isok(n) = (d=digits(n)) && ((n % vecsum(d)) == 0) && (vecsum(d) == prod(k=1, #d, d[k])); \\ Michel Marcus, Jan 02 2017