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A266816 Numbers whose arithmetic derivative is equal to the product of their digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 23:26 EDT 2021. Contains 348160 sequences. (Running on oeis4.)