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A190786 Numbers n such that sigma(2*n-1) = 3*n, where sigma(k) is the sum of the positive divisors of k. 0
8, 104, 512, 1488, 9680, 73728, 603680, 2508800, 1085407232, 29473106432 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All even perfect numbers are of the form z(2*z-1) with z = 2^(p-1), p prime and 2*z-1 = 2^p-1 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*c-1; 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

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Last modified January 27 18:06 EST 2022. Contains 350611 sequences. (Running on oeis4.)