A229238 Numbers k such that phi(sigma(k))/sigma(phi(k)) = 2.

2, 4, 16, 18, 64, 100, 450, 1458, 4096, 4624, 28900, 36450, 62500, 65536, 130050, 262144, 281250, 1062882, 1336336, 3334800, 7064400, 8352100, 10156800, 10534050, 18062500, 21193200, 22781250, 26572050, 37584450, 39062500, 48944016, 81281250, 124411716

Offset: 1

Author

Vladimir Letsko, Sep 17 2013

Keywords

• nonn

Comments

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.

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.

Examples

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

Links

• Donovan Johnson, Table of n, a(n) for n = 1..73

Crossrefs

Cf. A000010, A000203, A033632.

Programs

Maple

s:=n->phi(sigma(n))/sigma(phi(n));
for i to 9000000 do if s(i)=2 then print(i) fi od:

PARI

isok(n) = (eulerphi(sigma(n)) == 2*sigma(eulerphi(n))); \\ Michel Marcus, Sep 23 2013

Extensions

Extra term 4624 and more terms from Michel Marcus, Sep 23 2013