

A229238


Numbers n such that phi(sigma(n))/sigma(phi(n)) = 2.


3



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
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OFFSET

1,1


COMMENTS

2^k is in the sequence if and only if 2^{k+1}1 is Mersenne prime. In other words 2^k is the "even part" of 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.


LINKS

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


EXAMPLE

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


MAPLE

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


PROG

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


CROSSREFS

Cf. A033632, A000010, A000203.
Sequence in context: A186108 A131560 A067709 * A212202 A102545 A045521
Adjacent sequences: A229235 A229236 A229237 * A229239 A229240 A229241


KEYWORD

nonn


AUTHOR

Vladimir Letsko, Sep 17 2013


EXTENSIONS

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


STATUS

approved



