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A269719 Numbers whose arithmetic derivative is equal to the sum of some fixed power of their digits. 1
3, 4, 5, 7, 142, 581, 6127, 8549, 12643, 16999, 51703, 57121, 86833, 89195, 92029, 103039, 104647, 112093, 137317, 149851, 218269, 261883, 266923, 323723, 336273, 449881, 505891, 524371, 610171, 617569, 907873, 999643, 1119253, 1134227, 1728787, 1900523, 2045171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..37.

Paolo P. Lava, Terms of the sequence and their fixed power

EXAMPLE

3^0 = 1 and 3' = 1;

4^1 = 4 and 4' = 4;

1^3 + 4^3 + 2^3 = 73 and 143' = 73.

MAPLE

with(numtheory): P:= proc(q) local a, b, c, d, j, k, n, ok; for n from 3 to q do a:=[]; b:=n; ok:=0;

d:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]); a:=[]; b:=n; ok:=0;

for k from 1 to ilog10(n)+1 do if (b mod 10)>1 then ok:=1; fi; a:=[(b mod 10), op(a)]; b:=trunc(b/10); od; b:=-1; c:=0;

if ok=1 then while c<d do b:=b+1;

if b>0 then c:=add(a[k]^b, k=1..nops(a)); else for k from 1 to nops(a) do if a[k]=0 then c:=0; break;

else c:=c+1; fi; od; fi; od; if c=d then lprint(n, b); fi; fi; od; end: P(10^9);

MATHEMATICA

f[n_] := If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger@ Abs@ n]]; Select[Range[3, 10^5], Function[k, IntegerQ@ SelectFirst[Range[0, 10], Function[d, If[MemberQ[d, 0] && # == 0, Total@ Power[d /. 0 -> Nothing, #] == f@ k, Total@ Power[d, #] == f@ k]]@ IntegerDigits@ k &]]] (* Michael De Vlieger, Mar 04 2016, Version 10, f(n) after Michael Somos at A003415 *)

CROSSREFS

Cf. A003415.

Sequence in context: A101761 A035359 A325410 * A214626 A143593 A028267

Adjacent sequences:  A269716 A269717 A269718 * A269720 A269721 A269722

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, Mar 04 2016

STATUS

approved

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Last modified May 25 23:54 EDT 2019. Contains 323576 sequences. (Running on oeis4.)