A082731 a(n) is the smallest number k such that A033880(k)= n, or 0 if no such number exists, where A033880 is the abundance of k.

6, 0, 20, 18, 12, 0, 8925, 196, 56, 0, 40, 0, 24, 0, 272, 0, 550, 100, 208, 36, 176, 0, 1312, 0, 112, 0, 80, 0, 48, 0, 945, 15376, 572, 0, 928, 0, 2205, 0, 5696, 162, 736, 1352, 9555, 0, 350, 0, 490, 0, 60, 0, 416, 72, 352, 0, 90, 0, 84, 0, 160, 968, 96, 0, 24704, 0, 108, 200

Offset

0,1

Comments

Caution: so far a(n)=0 only indicates no k < 3*10^6 exists; nonexistence is not proved. - R. J. Mathar, Jul 26 2007

For each term listed as 0 in the Data section, there is no such k < 10^14. - Jon E. Schoenfield, Jan 12 2021

Links

Table of n, a(n) for n=0..65.

F. Firoozbakht and M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.

Maple

A082731 := proc(n) local k; k := 1 ; while numtheory[sigma](k)-2*k <> n do k := k+1 ; if k = 3000000 then RETURN(0) ; fi ; od ; RETURN(k) ; end: seq(A082731(n), n=0..200) ; # R. J. Mathar, Nov 07 2016

Crossrefs

Cf. A082730.

Sequence in context: A167356 A219540 A292497 * A272673 A167357 A064381

Adjacent sequences: A082728 A082729 A082730 * A082732 A082733 A082734

Keyword

nonn

Author

Amarnath Murthy, Apr 14 2003

Extensions

More terms from R. J. Mathar, Jul 26 2007

Status

approved