A291597 - OEIS

%I #25 Aug 31 2017 19:17:51

%S 5865,10005,15045,28815,37995,45645,50235,170085,310845,347565,521985,

%T 613785,627555,707115,791265,797385,830415,873885,994755,1014645,

%U 1066665,1078815,1202835,1323705,1366545,1542495,1689465,1730865,1819605,2001495,2013735,2246295,2264655

%N Numbers n such that cototient(n) does not divide phi(n!).

%C Terms are 3*5*17*23, 3*5*23*29, 3*5*17*59, 3*5*17*113, ...

%C Terms are not prime powers as cototient(p^k) = p^(k-1) which divides phi(n!). - _Chai Wah Wu_, Aug 30 2017

%H Chai Wah Wu, <a href="/A291597/b291597.txt">Table of n, a(n) for n = 1..45</a>

%e 5865 is a term because 5865 - phi(5865) = 3049 and phi(5865!) is not divisible by 3049.

%e 45645 is a term because 45645 - phi(45645) = 22861 and phi(45645!) is not divisible by 22861.

%o (PARI) valp(n, p)=my(s); while(n\=p, s+=n); s

%o is(n)=my(m=n-eulerphi(n), t, u); forprime(p=2, n, t=valp(n, p)-1; if(t && (u=valuation(m,p)), m/=p^min(t,u); if(m==1, return(0))); t=gcd(m,p-1); if(t>1, m/=t; if(m==1, return(0)))); m>1 \\ _Charles R Greathouse IV_, Aug 27 2017

%Y Cf. A000010, A048855, A051953.

%K nonn

%O 1,1

%A _Altug Alkan_, Aug 27 2017

%E a(8)-a(22) from _Charles R Greathouse IV_, Aug 27 2017

%E a(23)-a(29) from _Chai Wah Wu_, Aug 29 2017

%E a(30)-a(33) from _Chai Wah Wu_, Aug 30 2017