OFFSET
1,2
COMMENTS
Conjecture: For n > 1, a(n) is a Zumkeller number (A083207) [confirmed for n up to 47]. - Ivan N. Ianakiev, Sep 22 2017
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..180 (terms < 10^12; first 101 terms from Michel Marcus)
FORMULA
Let m be an odd number, z = A007733(m) and k, 0 <= k < z, be such that phi(m) == 2^k (mod m); then m*2^(i*z - k + 1) belongs to this sequence for all i >= 1. And this is a general form of the terms of this sequence.
Some families of solutions of the form m*2^(i*z - k + 1):
If m = 3, then z = 2 and k = 1 ==> 3*2^(2*i) is a term for all i >= 1.
If m = 5, then z = 4 and k = 2 ==> 5*2^(4*i-1) is a term for all i >= 1.
If m = 7, then z = 3 but k does not exist ==> no term with odd part equal to 7.
If m = 15, then z = 4 and k = 3 ==> 15*2^(4*i-2) is a term for all i >= 1.
If m = 77, then z = 30 and k = 14 ==> 77*2^(30*i-13) is a term for all i >= 1.
EXAMPLE
704 = 11*2^6 is a term since phi(11*2^6) = 5*2^6 and 11*2^6 divides 2^(5*2^6) - 5*2^6.
MATHEMATICA
{1}~Join~Select[Range[10^6], Function[n, # == PowerMod[2, #, n] &@ EulerPhi@ n]] (* Michael De Vlieger, Sep 18 2017 *)
PROG
(PARI) isok(n) = Mod(2, n)^eulerphi(n)==eulerphi(n);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Max Alekseyev and Altug Alkan, Sep 18 2017
STATUS
approved