A272857 Least k>1 such that the Euler totient function of powers k^e, 1 <= e <= n, are divisible by the number their divisors, d(k^e).

3, 3, 13, 61, 61, 421, 2521, 2521, 2521, 55441, 55441, 4324321, 4324321, 4324321, 4324321, 85765681, 85765681, 232792561, 232792561, 232792561, 232792561

Offset: 1

Author

Paolo P. Lava, May 12 2016

Keywords

• nonn
• more

Comments

a(22) <= 10708457761. - Amiram Eldar, May 27 2024

Examples

			phi(3) / d(3) = 2 / 2 = 1, phi(3^2) / d(3^2) = 6 / 3 = 2 but phi(3^3) / d(3^3) = 18 / 4 = 9 / 2;
phi(13) / d(13) = 12 / 2 = 6, phi(13^2) / d(13^2) = 156 / 3 = 52, phi(13^3) / d(13^3) = 2028 / 4 = 507 but phi(13^4) / d(13^4) = 26364 / 5.
		

Crossrefs

Cf. A000005, A000010, A070858, A272980, A272981.

Programs

Maple

with(numtheory): P:= proc(q) local a, j, k, ok, p; global n; a:=2;
for k from 1 to q do for n from a to q do ok:=1;
for j from 1 to k do if not type(phi(n^j)/tau(n^j), integer) then ok:=0; break; fi; od;
if ok=1 then a:=n; print(n); break; fi; od; od; end: P(10^9);