A246775 Smallest number x such that phi(x) = phi(x(n)), where x(n) is the n-th arithmetic derivatives of x and x is not equal to x(n).

2, 104, 15, 2565, 4947, 2827, 2834, 153, 3462, 16109, 3201, 7413, 31842, 24541, 66563, 15111, 223995, 542270, 733502, 717874, 521666, 2622290, 2111642, 16169763

Offset

1,1

Links

Table of n, a(n) for n=1..24.

Example

First 5 arithmetic derivatives of x = 4947 are 1991, 192, 640, 2368, 7168 and phi(4947) = phi(7178) = 3072.
First 9 arithmetic derivatives of x = 3462 are 2891, 875, 650, 635, 132, 188, 192, 640, 2368 and phi(3462) = phi(2368) = 1152.

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 phi(k)=phi(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]; aQ[x_, n_] := Module[{xx = dd[x, n]}, xx != x && EulerPhi[x] == EulerPhi[xx]]; a[n_] := Module[{k = 1}, While[! aQ[k, n], k++]; k]; Array[a, 10] (* Amiram Eldar, Apr 06 2019 *)

Crossrefs

Cf. A000203, A003415, A246774.

Sequence in context: A215964 A106299 A176933 * A281053 A101530 A199945

Adjacent sequences: A246772 A246773 A246774 * A246776 A246777 A246778

Keyword

nonn,more

Author

Paolo P. Lava, Sep 03 2014

Extensions

a(17)-a(24) from Amiram Eldar, Apr 06 2019

Status

approved