A291597 Numbers n such that cototient(n) does not divide phi(n!).

5865, 10005, 15045, 28815, 37995, 45645, 50235, 170085, 310845, 347565, 521985, 613785, 627555, 707115, 791265, 797385, 830415, 873885, 994755, 1014645, 1066665, 1078815, 1202835, 1323705, 1366545, 1542495, 1689465, 1730865, 1819605, 2001495, 2013735, 2246295, 2264655

Offset: 1

Author

Altug Alkan, Aug 27 2017

Keywords

• nonn

Comments

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

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

Examples

			5865 is a term because 5865 - phi(5865) = 3049 and phi(5865!) is not divisible by 3049.
45645 is a term because 45645 - phi(45645) = 22861 and phi(45645!) is not divisible by 22861.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..45

Crossrefs

Cf. A000010, A048855, A051953.

Programs

PARI

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

Extensions

a(8)-a(22) from Charles R Greathouse IV, Aug 27 2017

a(23)-a(29) from Chai Wah Wu, Aug 29 2017

a(30)-a(33) from Chai Wah Wu, Aug 30 2017