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A291548
Numbers k such that uphi(k) does not divide uphi(k!).
0
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, ...
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
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