A229209 Numbers k such that Sum_{j=1..k} phi(j)^j == 0 (mod k).

1, 2, 5, 7, 11, 39, 126, 266, 683, 2514, 12929

Offset: 1

Author

Paolo P. Lava, Sep 16 2013

Keywords

• nonn
• more

Comments

Tested up to k = 600000. - Jinyuan Wang, Feb 19 2021

Examples

			phi(1)^1 + phi(2)^2 + phi(3)^3 + phi(4)^4 + phi(5)^5 = 1^1 + 1^2 + 2^3 + 2^4 + 4^5 = 1050 and 1050/5 = 210.
		

Crossrefs

Cf. A000010, A227427, A227429, A227502, A227848, A229095, A229207, A229208, A229210, A229211.

Programs

Maple

with(numtheory); P:=proc(q) local n, t; t:=0;
for n from 1 to q do t:=t+phi(n)^n; if t mod n=0 then print(n);
fi; od; end: P(10^6);

PARI

is(k) = sum(i=1, k, Mod(eulerphi(i), k)^i) == 0; \\ Jinyuan Wang, Feb 19 2021