A291548 - OEIS

%I #28 Jan 28 2024 15:09:11

%S 4,8,24,27,32,96,2187,8192,24576,131072,155648,393216,524288,655360,

%T 917504,1572864,1594323,3188646,6377292,48828125,97656250,341796875,

%U 390625000,1220703125,2147483648,2441406250,6442450944

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

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

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

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

%o uphi(n,f=factor(n))=prod(i=1,#f~, f[i,1]^f[i,2]-1)

%o 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

%Y Cf. A047994.

%K nonn

%O 1,1

%A _Altug Alkan_, Aug 26 2017

%E a(10)-a(19) from _Charles R Greathouse IV_, Aug 27 2017

%E a(20) from _Charles R Greathouse IV_, Sep 06 2017

%E a(21) from _Charles R Greathouse IV_, Oct 12 2017

%E a(22)-a(27) from _Max Alekseyev_, Jan 28 2024