A331182 - OEIS

%I #10 Jan 12 2022 03:21:14

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

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

%U 1,1,1,1,1,11,2,7,1,1,1,2,2,12,1,1,2,13,2,4,1,1,1,8,3,14,1,1,1,2,2,1,1,1,1,5,1

%N Number of values of k, 1 <= k <= n, with A083254(k) = A083254(n), where A083254(n) = 2*phi(n) - n.

%C Ordinal transform of A083254.

%H Antti Karttunen, <a href="/A331182/b331182.txt">Table of n, a(n) for n = 1..65537</a>

%t Module[{b}, b[_] = 0;

%t a[n_] := With[{t = 2 EulerPhi[n] - n}, b[t] = b[t] + 1]];

%t Array[a, 105] (* _Jean-François Alcover_, Jan 12 2022 *)

%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 A083254(n) = (2*eulerphi(n)-n);

%o v331182 = ordinal_transform(vector(up_to,n,A083254(n)));

%o A331182(n) = v331182[n];

%Y Cf. A000010, A083254.

%Y Cf. also A081373, A331175, A331181.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jan 11 2020