A096823 a(n) = p*(p+(2n-1))/2, where p = A096822(n) is the smallest primes of form 2^x-(2n-1).

6, 20, 12, 151115727449904501489664, 56, 40, 24, 272, 1504, 208, 176, 1312, 112, 80, 48, 6208, 992, 928, 2059264, 5696, 736, 144115176533131264, 608, 544, 5056, 416, 352, 4672, 224, 160, 96, 24704, 24448, 3904, 3776, 487936, 112384, 3392, 22912

Offset

1,1

Comments

These numbers are clearly analogous to perfect numbers.

sigma(a(n)) mod a(n) = 2*n.

Links

Table of n, a(n) for n=1..39.

Example

a(1) = 6 is the first even perfect number;
a(7) = 24 corresponds to A096821(1) = 24;
a(4) = 151115727449904501489664 = 2^38*(2^39-7) = 274877906944*549755813881;

Crossrefs

Cf. A096502, A096821, A096822.

Sequence in context: A090590 A002566 A087998 * A321328 A007253 A096897

Adjacent sequences: A096820 A096821 A096822 * A096824 A096825 A096826

Keyword

nonn

Author

Labos Elemer, Jul 13 2004

Extensions

Edited by Max Alekseyev, May 29 2025

Status

approved