OFFSET
1,1
COMMENTS
This sequence is infinite, since it contains all the numbers of the form 2^4*5^k, for k>0. The key fact is that phi(2^4*5^k) = 2^5*5^(k-1), so only 5 moduli do not vanish. - Giovanni Resta, May 25 2016
EXAMPLE
Divisors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693 and its Euler totient function is phi(693) = 360. Then 360 mod 1 = 0, 360 mod 3 = 0, 360 mod 7 = 3, 360 mod 9 = 0, 360 mod 11 = 8, 360 mod 21 = 3, 360 mod 33 = 30, 360 mod 63 = 45, 360 mod 77 = 52, 360 mod 99 = 63, 360 mod 231 = 129, 360 mod 693 = 360 and 0 + 0 + 3 + 0 + 8 + 3 + 30 + 45 + 52 + 63 + 129 + 360 = 693.
MAPLE
with(numtheory): P:=proc(q) local a, k, n; for n from 1 to q do a:=divisors(n);
if add(phi(n) mod a[k], k=1..nops(a))=n then print(n); fi; od; end: P(10^9);
MATHEMATICA
Select[Range[10^5], # == Plus @@ Mod[EulerPhi@ #, Divisors@ #] &] (* Giovanni Resta, May 25 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 19 2016
EXTENSIONS
a(17)-a(30) from Giovanni Resta, May 25 2016
STATUS
approved