

A190786


Numbers n such that sigma(2*n1) = 3*n, where sigma(k) is the sum of the positive divisors of k.


0




OFFSET

1,1


COMMENTS

All even perfect numbers are of the form z(2*z1) with z = 2^(p1), p prime and 2*z1 = 2^p1 prime. It is unknown if there are any odd perfect numbers of this same form. The equation defining the sequence appears while working a special case of the conjecture.
It is conjectured that all terms of this sequence are even numbers.
a(11) > 5*10^11, according to Giovanni Resta at A063906.  Amiram Eldar, Jan 27 2019


LINKS

Table of n, a(n) for n=1..10.


FORMULA

a(n) = (A063906(n)+1)/2.  Amiram Eldar, Jan 27 2019


EXAMPLE

Example: a(1)=8 since sigma(15)= 24 = 3*8.


MATHEMATICA

Select[Range[10^5], DivisorSigma[1, 2#  1] == 3# &] (* Alonso del Arte, May 19 2011 *)


PROG

(PARI) zt(a, b) = {local(c, c1, c2, s); c =a ; c1 = 2*c1; c2 = 3*c; while(c<b, s = sigma(c1); if(s == c2, print(c); ); c1 = c1 +2; c2 = c2 +3; c = c+1); }


CROSSREFS

Cf. A000203, A000396, A063906.
Sequence in context: A297069 A090237 A222664 * A138430 A164760 A335608
Adjacent sequences: A190783 A190784 A190785 * A190787 A190788 A190789


KEYWORD

nonn,more


AUTHOR

Luis H. Gallardo, May 19 2011


EXTENSIONS

a(9)a(10) added from the data at A063906 by Amiram Eldar, Jan 27 2019


STATUS

approved



