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

1,1

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A000010, A048855, A051953.

Sequence in context: A212478 A333232 A053340 * A233945 A264216 A061735

Adjacent sequences: A291594 A291595 A291596 * A291598 A291599 A291600

Keyword

nonn

Author

Altug Alkan, 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

Status

approved