A331177 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).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 11 2020

Keywords

• nonn

Comments

Ordinal transform of A319677.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A047994, A319677.

Cf. also A330739, A331175.

Programs

PARI

up_to = 65537;
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; };
A047994(n) = { my(f=factor(n)); prod(i=1, #f~, (f[i, 1]^f[i, 2])-1); };
A319677(n) = n/gcd(n, A047994(n));
v331177 = ordinal_transform(vector(up_to, n, A319677(n)));
A331177(n) = v331177[n];