A096823 - OEIS

A096823

Numbers of the form p*(p+(2n-1))/2 created with smallest primes of form p=2^x-(2n-1)=A096522(n). Here the exponent equals x=A096502[n], the least exponent providing this kind of primes. Peculiarity of the present terms is as follows: Mod[sigma[a(n)],a[n]]=2*n.

%I #3 Oct 15 2013 22:32:27

%S 6,20,12,151115727449904501489664,56,40,24,272,1504,208,176,1312,112,

%T 80,48,6208,992,928,2059264,5696,736,144115176533131264,608,544,5056,

%U 416,352,4672,224,160,96,24704,24448,3904,3776,487936,112384,3392,22912

%N Numbers of the form p*(p+(2n-1))/2 created with smallest primes of form p=2^x-(2n-1)=A096522(n). Here the exponent equals x=A096502[n], the least exponent providing this kind of primes. Peculiarity of the present terms is as follows: Mod[sigma[a(n)],a[n]]=2*n.

%C These numbers are clearly analogous to perfect numbers.

%e a[1]=6 is the first even perfect number;

%e a[7]=24 corresponds to A096821(1)=24;

%e a[4]=151115727449904501489664=2^38*(2^39-7)=274877906944*549755813881;

%Y Cf. A096502, A096821, A096822.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 13 2004