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

1,2

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Harshad Numbers

Example

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

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 *)

Prog

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

Crossrefs

Intersection of A005349 and A034710.

Cf. A038186.

Sequence in context: A004871 A059405 A191872 * A001104 A151544 A032561

Adjacent sequences: A280352 A280353 A280354 * A280356 A280357 A280358

Keyword

nonn,base,easy

Author

Ilya Gutkovskiy, Jan 01 2017

Status

approved