|
|
A049559
|
|
a(n) = gcd(n - 1, phi(n)).
|
|
34
|
|
|
1, 1, 2, 1, 4, 1, 6, 1, 2, 1, 10, 1, 12, 1, 2, 1, 16, 1, 18, 1, 4, 1, 22, 1, 4, 1, 2, 3, 28, 1, 30, 1, 4, 1, 2, 1, 36, 1, 2, 1, 40, 1, 42, 1, 4, 1, 46, 1, 6, 1, 2, 3, 52, 1, 2, 1, 4, 1, 58, 1, 60, 1, 2, 1, 16, 5, 66, 1, 4, 3, 70, 1, 72, 1, 2, 3, 4, 1, 78, 1, 2, 1, 82, 1, 4, 1, 2, 1, 88, 1, 18, 1, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
For prime n, a(n) = n - 1. Question: do nonprimes exist with this property?
Lehmer's totient problem (1932): are there composite numbers n such that a(n) = phi(n)? - Thomas Ordowski, Nov 08 2015
|
|
REFERENCES
|
Richard K. Guy, Unsolved Problems in Number Theory, B37.
|
|
LINKS
|
|
|
FORMULA
|
a(p^m) = a(p) = p - 1 for prime p and m > 0. - Thomas Ordowski, Dec 10 2013
(End)
|
|
EXAMPLE
|
a(9) = 2 because phi(9) = 6 and gcd(8, 6) = 2.
a(10) = 1 because phi(10) = 4 and gcd(9, 4) = 1.
|
|
MAPLE
|
seq(igcd(n-1, numtheory:-phi(n)), n=1..100); # Robert Israel, Nov 09 2015
|
|
MATHEMATICA
|
|
|
PROG
|
(Python)
from sympy import totient, gcd
print([gcd(totient(n), n - 1) for n in range(1, 101)]) # Indranil Ghosh, Mar 27 2017
|
|
CROSSREFS
|
Cf. A000010, A002322, A039766, A063994, A160595, A209211, A219428, A264012, A264024, A280262, A283656, A283872, A284089, A284440, A318827, A318829, A318830, A330747 (ordinal transform), A340195.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|