A303757 - OEIS

%I #15 Nov 24 2018 01:28:39

%S 1,1,1,2,1,3,1,2,2,3,1,4,1,3,1,2,1,4,1,3,2,2,1,4,1,3,2,4,1,5,1,2,2,3,

%T 1,5,1,3,2,4,1,6,1,3,3,2,1,5,2,4,1,4,1,4,2,5,2,2,1,6,1,2,3,2,1,5,1,3,

%U 1,6,1,7,1,4,3,5,2,8,1,4,1,4,1,9,1,3,1,5,1,10,2,2,3,2,3,5,1,4,4,6,1,6,1,2,3

%N a(1) = 1 and for n > 1, a(n) = number of values of k, 2 <= k <= n, with A000010(k) = A000010(n), where A000010 is Euler totient function phi.

%C Ordinal transform of f, where f(1) = 0 and f(n) = A000010(n) for n > 1.

%C After a(1)=1 and a(4)=2, the positions of the rest of records is given by A081375(n) = 6, 12, 30, 42, 72, 78, 84, 90, 190, ..., for n >= 3.

%C Apart from a(2) = 1, the other positions of 1's is given by A210719.

%H Antti Karttunen, <a href="/A303757/b303757.txt">Table of n, a(n) for n = 1..65537</a>

%F Except for a(2) = 1, a(n) = A081373(n).

%t With[{s = EulerPhi@ Range@ 105}, MapAt[# + 1 &, Table[Count[s[[2 ;; n]], _?(# == s[[n]] &)], {n, Length@ s}], 1]] (* _Michael De Vlieger_, Nov 23 2018 *)

%o (PARI)

%o up_to = 65537;

%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };

%o Aux303757(n) = if(1==n,0,eulerphi(n));

%o v303757 = ordinal_transform(vector(up_to,n,Aux303757(n)));

%o A303757(n) = v303757[n];

%Y Cf. A000010, A081373, A081375, A210719, A303754, A303758, A303777.

%K nonn

%O 1,4

%A _Antti Karttunen_, Apr 30 2018