A291548 Numbers k such that uphi(k) does not divide uphi(k!).

4, 8, 24, 27, 32, 96, 2187, 8192, 24576, 131072, 155648, 393216, 524288, 655360, 917504, 1572864, 1594323, 3188646, 6377292, 48828125, 97656250, 341796875, 390625000, 1220703125, 2147483648, 2441406250, 6442450944

Offset

1,1

Comments

Terms are 2^2, 2^3, 3*2^3, 3^3, 2^5, 3*2^5, 3^7, 2^13, 3*2^13, ...

Links

Table of n, a(n) for n=1..27.

Example

4 is a term because uphi(4) = 3 does not divide uphi(4!) = 14.

Prog

(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
uphi(n, f=factor(n))=prod(i=1, #f~, f[i, 1]^f[i, 2]-1)
is(n)=my(m=uphi(n), t); forprime(p=2, n, t=gcd(lift(Mod(p, m)^valp(n, p)-1), m); if(t>1, m/=t; if(m==1, return(0)))); m>1 \\ Charles R Greathouse IV, Aug 27 2017

Crossrefs

Cf. A047994.

Sequence in context: A362212 A254731 A368903 * A212019 A075708 A066617

Adjacent sequences: A291545 A291546 A291547 * A291549 A291550 A291551

Keyword

nonn

Author

Altug Alkan, Aug 26 2017

Extensions

a(10)-a(19) from Charles R Greathouse IV, Aug 27 2017

a(20) from Charles R Greathouse IV, Sep 06 2017

a(21) from Charles R Greathouse IV, Oct 12 2017

a(22)-a(27) from Max Alekseyev, Jan 28 2024

Status

approved