

A202855


Numbers n such that phi(n)  1 divides n, where phi is Euler's totient function.


6




OFFSET

1,1


COMMENTS

a(10) > 10^11.  Donovan Johnson, Dec 29 2011
The sequence b(n) = 4*A050474(n) is a subsequence of this sequence, and comprises solutions of n/(phi(n)  1) = 4, accounting for all terms up to a(9) except a(1) and a(3). Proof: suppose n/(phi(n)  1) = 4. With n = 4*x, x/(phi(4*x)  1) = 1, or phi(4*x) = x + 1. Since phi(k) is even for k > 2, x is odd, and phi(4*x) = 2*phi(x) = x + 1, the definition of A050474. It follows that 4*A050474(8) = 27971850688528380 is a term of this sequence.  Chris Boyd, Mar 22 2015
a(10) > 10^13.  Giovanni Resta, Jul 13 2015


LINKS

Table of n, a(n) for n=1..9.


MATHEMATICA

Select[1 + Range[1000000], Divisible[#, EulerPhi[#]  1] &]


PROG

(PARI) for(n=3, 1e7, if(n%(eulerphi(n)1)==0, print1(n", "))) \\ Charles R Greathouse IV, Dec 26 2011


CROSSREFS

Cf. A000010, A050474, A203966.
Sequence in context: A255733 A137333 A006719 * A182857 A251483 A009287
Adjacent sequences: A202852 A202853 A202854 * A202856 A202857 A202858


KEYWORD

nonn,more


AUTHOR

José María Grau Ribas, Dec 25 2011


EXTENSIONS

a(8) from Charles R Greathouse IV, Dec 27 2011
a(9) from Donovan Johnson, Dec 29 2011


STATUS

approved



