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A281707 Even integers k such that phi(sum of even divisors of k) = sum of odd divisors of k. 2
6, 14, 42, 62, 186, 254, 434, 762, 1302, 1778, 5334, 7874, 16382, 23622, 49146, 55118, 114674, 165354, 262142, 344022, 507842, 786426, 1048574, 1523526, 1834994, 2080514, 3145722, 3554894, 5504982, 6241542, 7340018, 8126402, 10664682, 14563598, 22020054 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The number of divisors of a(n) is a power of 2, and sum of even divisors = 2^(m+1), sum of odd divisors = 2^m for some m.

a(n) == 2, 6 mod 8 or a(n) == 2, 6 mod 12.

a(n) is of the form 2p1*p2*...pk where p1, p2,...,pk are Mersenne primes =   3, 7, 31, 127, 8191,... (see A000668).

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

62 is in the sequence because the divisors are 1, 2, 31 and 62. Sum of even divisors of 62 = 62 + 2 = 2^6, sum of odd divisors = 1 + 31 = 2^5 => phi(2^6) = 2^5.

MAPLE

with(numtheory):

for n from 2 by 2 to 10^6 do:

x:=divisors(n):n1:=nops(x):s0:=0:s1:=0:

   for k from 1 to n1 do:

    if irem(x[k], 2)=0

     then

     s0:=s0+ x[k]:

     else

     s1:=s1+ x[k]:

    fi:

  od:

    if s1=phi(s0)

     then

     print(n):

     else

    fi:

od:

PROG

(PARI) isok(n) = eulerphi(sumdiv(n, d, d*((d % 2)==0))) == sumdiv(n, d, d*(d%2)); \\ Michel Marcus, Jan 28 2017

CROSSREFS

Cf. A000010, A000593, A000668, A146076.

Sequence in context: A134259 A069166 A184393 * A093369 A130443 A294655

Adjacent sequences:  A281704 A281705 A281706 * A281708 A281709 A281710

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jan 28 2017

STATUS

approved

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Last modified March 21 21:34 EDT 2019. Contains 321382 sequences. (Running on oeis4.)