login
Number of values of k, 1 <= k <= n, with A063994(k) = A063994(n), where A063994(n) = Product_{primes p dividing n} gcd(p-1, n-1).
2

%I #14 Jan 12 2022 03:21:19

%S 1,2,1,3,1,4,1,5,2,6,1,7,1,8,2,9,1,10,1,11,3,12,1,13,4,14,3,1,1,15,1,

%T 16,5,17,6,18,1,19,7,20,1,21,1,22,1,23,1,24,2,25,8,2,1,26,9,27,10,28,

%U 1,29,1,30,11,31,2,1,1,32,12,3,1,33,1,34,13,4,14,35,1,36,4,37,1,38,3,39,15,40,1,41,2,42,16

%N Number of values of k, 1 <= k <= n, with A063994(k) = A063994(n), where A063994(n) = Product_{primes p dividing n} gcd(p-1, n-1).

%C Ordinal transform of A063994.

%H Antti Karttunen, <a href="/A330756/b330756.txt">Table of n, a(n) for n = 1..65537</a>

%t A063994[n_] := If[n==1, 1, Times @@ GCD[n-1, First /@ FactorInteger[n]-1]];

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

%t a[n_] := With[{t = A063994[n]}, b[t] = b[t]+1]];

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

%o (PARI)

%o up_to = 65537;

%o A063994(n) = { my(f=factor(n)[, 1]); prod(i=1, #f, gcd(f[i]-1, n-1)); }; \\ From A063994

%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 v330756 = ordinal_transform(vector(up_to, n, A063994(n)));

%o A330756(n) = v330756[n];

%Y Cf. A063994, A209211.

%Y Cf. also A081373, A303756, A330747.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 30 2019