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

1,3

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A035400 A235918 A071222 * A230849 A135517 A327395

Adjacent sequences: A067002 A067003 A067004 * A067006 A067007 A067008

Keyword

nonn

Author

Labos Elemer, Dec 22 2001

Status

approved