A266816 Numbers whose arithmetic derivative is equal to the product of their digits.

4, 11, 25, 329, 3383, 4343, 5561, 6623, 12773, 17267, 21479, 57721, 129383, 136259, 142943, 172793, 256631, 292571, 364823, 413663, 413927, 619337, 653291, 1215659, 1218863, 1268951, 1276931, 1483751, 1655219, 1892327, 2952731, 4158719, 4973531, 5418671, 6377663

Offset

1,1

Comments

4 appears to be the only even number in the sequence.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

4’ = 4;
11’ = 1 = 1*1;
25’ = 10 = 2*5;
329’ = 54 = 3*2*9; etc.

Maple

with(numtheory):  P:=proc(q) local a, b, k, n; for n from 1 to q do a:=n; b:=1;
for k from 1 to ilog10(n)+1 do b:=b*(a mod 10); a:=trunc(a/10); od;
if n*add(op(2, a)/op(1, a), a=ifactors(n)[2])=b then print(n); fi; od; end: P(10^9);

Mathematica

Select[Range[3, 10^5], Times @@ IntegerDigits@ # == # Total[#2/#1 & @@@
FactorInteger@ Abs@ #] &] (* Michael De Vlieger, Feb 10 2016, after Michael Somos at A003415 *)

Crossrefs

Cf. A003415, A007954, A058627, A145746.

Sequence in context: A202088 A328937 A328936 * A289082 A079467 A140897

Adjacent sequences: A266813 A266814 A266815 * A266817 A266818 A266819

Keyword

nonn,base

Author

Paolo P. Lava, Feb 10 2016

Status

approved