A229210 - OEIS

%I #23 Feb 14 2021 16:26:47

%S 1,2,5,24,36,371,445,1578,3616,9292,38123,142815,184097

%N Numbers k such that Sum_{i=1..k} (i-tau(i))^i == 0 (mod k), where tau(i) = A000005(i), the number of divisors of i, and i-tau(i) = A049820(i).

%C a(12) > 50000.

%C a(14) > 200000. - _Michel Marcus_, Feb 25 2016

%e (1 - tau(1))^1 + (2 - tau(2))^2 + ... + (5 - tau(5))^5 = 245 and 245 / 5 = 49.

%p with(numtheory); P:=proc(q) local n, t; t:=0;

%p for n from 1 to q do t:=t+(n-tau(n))^n; if t mod n=0 then print(n);

%p fi; od; end: P(10^6);

%o (PARI) isok(n) = sum(i=1, n, Mod(i-numdiv(i), n)^i) == 0; \\ _Michel Marcus_, Feb 25 2016

%Y Cf. A000010, A227427, A227429, A227502, A227848, A229095, A229207-A229209, A229211.

%K nonn,more

%O 1,2

%A _Paolo P. Lava_, Sep 16 2013

%E Name corrected by _Michel Marcus_, Feb 25 2016

%E a(12)-a(13) from _Michel Marcus_, Feb 25 2016