A229238 - OEIS

%I #21 Jun 22 2022 01:26:00

%S 2,4,16,18,64,100,450,1458,4096,4624,28900,36450,62500,65536,130050,

%T 262144,281250,1062882,1336336,3334800,7064400,8352100,10156800,

%U 10534050,18062500,21193200,22781250,26572050,37584450,39062500,48944016,81281250,124411716

%N Numbers k such that phi(sigma(k))/sigma(phi(k)) = 2.

%C 2^j is in the sequence if and only if 2^{j+1}-1 is a Mersenne prime. In other words 2^j is the "even part" of a perfect number. Thus we have some generalization of perfect numbers.

%C Odd prime divisors of the first 19 terms of a(n) are exclusively 3, 5, 17, i.e., Fermat's primes, but 3334800 = 2^4*3*5^2*7*397.

%H Donovan Johnson, <a href="/A229238/b229238.txt">Table of n, a(n) for n = 1..73</a>

%e 18 is in the sequence because phi(sigma(18)) = phi(39) = 24 = 2*sigma(6) = 2*sigma(phi(18)).

%p s:=n->phi(sigma(n))/sigma(phi(n));

%p for i to 9000000 do if s(i)=2 then print(i) fi od:

%o (PARI) isok(n) = (eulerphi(sigma(n)) == 2*sigma(eulerphi(n))); \\ _Michel Marcus_, Sep 23 2013

%Y Cf. A000010, A000203, A033632.

%K nonn

%O 1,1

%A _Vladimir Letsko_, Sep 17 2013

%E Extra term 4624 and more terms from _Michel Marcus_, Sep 23 2013