A190786 Numbers m such that sigma(2*m-1) = 3*m, where sigma(k) is the sum of the positive divisors of k.

8, 104, 512, 1488, 9680, 73728, 603680, 2508800, 1085407232, 29473106432, 583166845500512, 18236498181611824400

Offset: 1

Author

Luis H. Gallardo, May 19 2011

Keywords

• nonn
• more

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.

Examples

			a(1)=8 is a term since sigma(15) = 24 = 3*8.
		

Crossrefs

Cf. A000203, A000396, A063906.

Programs

Mathematica

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

PARI

zt(a,b) = {local(c,c1,c2,s); c =a ; c1 = 2*c-1;c2 = 3*c;while(c
				

Formula

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

Extensions

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

a(11) from Max Alekseyev, May 22 2025

a(12) from Max Alekseyev, Jul 30 2025