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%I #54 Apr 25 2021 17:24:23
%S 0,1,2,2,4,2,6,4,6,4,10,2,12,6,4,4,16,6,18,4,6,10,22,4,20,12,18,6,28,
%T 4,30,8,10,16,12,6,36,18,12,4,40,6,42,10,12,22,46,4,42,20,16,12,52,18,
%U 20,6,18,28,58,4,60,30,6,16,12,10,66,16,22,12,70,6,72,36,20,18,30
%N Smallest m such that b^phi(n) == b^m (mod n) for every integer b, where phi(n) = A000010(n).
%C It suffices to check all bases 1 <= b <= n.
%C For n > 1; if A002322(n) = phi(n), then a(n) = phi(n). So a(p) = p-1 for all primes p.
%C Numbers n > 1 such that a(n) < phi(n) are A033949 > 8.
%C Conjecture: a(n) > A002322(n) only for n = 8 and 24.
%H Antti Karttunen (terms 1..4000) & Altug Alkan, <a href="/A277030/b277030.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjectured: a(n) = A002322(n), except for a(1) = 0 and a(8) = a(24) = 4.
%o (PARI) A277030(n) = { my(b,m=0); if(1==n,0,while(1, m=m+1; b=1; while(((b^eulerphi(n))%n) == ((b^m)%n), b=b+1; if(b>n, return(m))))); }; \\ (Following the description). - _Antti Karttunen_, Jul 28 2017
%o (Python)
%o from sympy import totient
%o def a(n):
%o m=0
%o if n==1: return 0
%o else:
%o while True:
%o m+=1
%o b=1
%o while (b**totient(n))%n==(b**m)%n:
%o b+=1
%o if b>n: return m
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jul 29 2017, after PARI code
%Y Cf. A000010, A002322, A033949.
%K nonn
%O 1,3
%A _Thomas Ordowski_ and _Altug Alkan_, Sep 25 2016
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