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A246774 Smallest number x such that sigma(x) = sigma(x(n)), where x(n) is the n-th arithmetic derivatives of x and x is not equal to x(n). 1
60, 482, 3903, 5667, 175, 68951, 11039, 76939, 1157, 22746, 19847, 16195, 23806, 345855, 824059, 269862, 2484227, 809358, 94558183, 98337630, 6504935 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

First 5 arithmetic derivatives of x = 175 are 95, 24, 44, 48, 112 and sigma(175) = sigma(112) = 48.

First 9 arithmetic derivatives of x = 1157 are 102, 91, 20, 24, 44, 48, 112, 240, 608 and sigma(1157) = sigma(608) = 1260.

MAPLE

with(numtheory); P:= proc(q) local a, b, k, n, p, t;

for n from 1 to q do for k from 1 to q do t:=1; b:=k;

while t<=n do a:=b*add(op(2, p)/op(1, p), p=ifactors(b)[2]); b:=a; t:=t+1; od;

if sigma(k)=sigma(a) and k<>a then lprint(n, k); break; fi;

od; od; end: P(10^6);

MATHEMATICA

d[n_] := If[n < 2, 0, n*Total[#2/#1 & @@@ FactorInteger[n]]]; dd[n_, k_] := Nest [d, n, k]; sigma[x_] := If[x > 0, DivisorSigma[1, x], 0]; aQ[x_, n_] := Module[ {xx = dd[x, n]}, xx != x && sigma[x] == sigma[xx]]; a[n_] := Module[{k = 1}, While[!aQ[k, n], k++]; k]; Array[a, 10] (* Amiram Eldar, Apr 06 2019 *)

CROSSREFS

Cf. A000203, A003415, A246775.

Sequence in context: A088943 A097387 A057096 * A341597 A334306 A069140

Adjacent sequences:  A246771 A246772 A246773 * A246775 A246776 A246777

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Sep 03 2014

EXTENSIONS

a(15)-a(21) from Amiram Eldar, Apr 06 2019

STATUS

approved

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Last modified June 24 08:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)