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A229209
Numbers k such that Sum_{j=1..k} phi(j)^j == 0 (mod k).
4
1, 2, 5, 7, 11, 39, 126, 266, 683, 2514, 12929
OFFSET
1,2
COMMENTS
Tested up to k = 600000. - Jinyuan Wang, Feb 19 2021
EXAMPLE
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.
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);
PROG
(PARI) is(k) = sum(i=1, k, Mod(eulerphi(i), k)^i) == 0; \\ Jinyuan Wang, Feb 19 2021
KEYWORD
nonn,more
AUTHOR
Paolo P. Lava, Sep 16 2013
STATUS
approved