A067005 Totient of A061026(n) divided by n.

1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 2, 2, 1, 6, 1, 10, 1, 2, 1, 2, 1, 4, 2, 2, 1, 2, 1, 10, 1, 2, 3, 2, 1, 4, 5, 2, 1, 2, 1, 4, 1, 4, 1, 6, 1, 4, 2, 2, 1, 2, 1, 2, 1, 4, 1, 12, 1, 6, 5, 2, 1, 2, 1, 4, 2, 2, 1, 8, 1, 4, 2, 2, 3, 6, 1, 4, 1, 2, 1, 2, 1, 12, 2, 4, 1, 2, 2, 6, 1, 4, 3, 2, 1, 4, 2, 2, 1

Offset: 1

Author

Labos Elemer, Dec 22 2001

Keywords

• nonn

Examples

			n = 24: a(24) = 1 = phi(A061026(24))/24 = phi(35)/24 = 24/24;
n = 85: a(85) = 12 = phi(A061026(85))/85 = 1020/85.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Crossrefs

Cf. A000010, A061026, A066674, A066675, A066676, A066677, A066678.

Programs

Mathematica

Table[m = 1; While[! Divisible[Set[k, EulerPhi@ m], n], m++]; k/n, {n, 100}] (* Michael De Vlieger, Mar 18 2017 *)

PARI

for(n=1,100, s=1; while((e=eulerphi(s))%n>0, s++); print1(e/n ", ")); \\ Zak Seidov, Feb 22 2014

PARI

list(len) = {my(v = vector(len), c = 0, k = 1, e); while(c < len, e = eulerphi(k); fordiv(e, d, if(d <= len && v[d] == 0, v[d] = e/d; c++)); k++); v; } \\ Amiram Eldar, Mar 08 2025

Python

from sympy.ntheory import totient
def k(n):
    m=1
    while totient(m)%n: m+=1
    return m
print([totient(k(n))//n for n in range(1, 101)]) # Indranil Ghosh, Mar 18 2017

Formula

a(n) = A000010(A061026(n))/n.

a(n) = A066678(n)/n. - Amiram Eldar, Mar 08 2025