A229210 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).

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

Offset: 1

Author

Paolo P. Lava, Sep 16 2013

Keywords

• nonn
• more

Comments

a(12) > 50000.

a(14) > 200000. - Michel Marcus, Feb 25 2016

Examples

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

Crossrefs

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

Programs

Maple

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

PARI

isok(n) = sum(i=1, n, Mod(i-numdiv(i), n)^i) == 0; \\ Michel Marcus, Feb 25 2016

Extensions

Name corrected by Michel Marcus, Feb 25 2016

a(12)-a(13) from Michel Marcus, Feb 25 2016