A331177 - OEIS

%I #5 Jan 11 2020 21:50:37

%S 1,1,1,1,1,2,1,1,1,2,1,2,1,2,1,1,1,2,1,3,3,2,1,1,1,2,1,1,1,2,1,1,1,2,

%T 1,3,1,2,3,1,1,4,1,1,1,2,1,2,1,2,1,4,1,2,3,2,3,2,1,4,1,2,1,1,1,2,1,3,

%U 1,2,1,3,1,2,3,1,1,5,1,3,1,2,1,5,1,2,1,1,1,2,1,1,3,2,1,1,1,2,1,4,1,2,1,1,3

%N Number of values of k, 1 <= k <= n, with A319677(k) = A319677(n), where A319677(n) = n/gcd(n, uphi(n)), and uphi is unitary totient function (A047994).

%C Ordinal transform of A319677.

%H Antti Karttunen, <a href="/A331177/b331177.txt">Table of n, a(n) for n = 1..65537</a>

%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 A047994(n) = { my(f=factor(n)); prod(i=1, #f~, (f[i, 1]^f[i, 2])-1); };

%o A319677(n) = n/gcd(n, A047994(n));

%o v331177 = ordinal_transform(vector(up_to, n, A319677(n)));

%o A331177(n) = v331177[n];

%Y Cf. A047994, A319677.

%Y Cf. also A330739, A331175.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jan 11 2020