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A291597 Numbers n such that cototient(n) does not divide phi(n!). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 15 01:47 EDT 2020. Contains 336485 sequences. (Running on oeis4.)