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

Author

Amarnath Murthy, Apr 14 2003

Keywords

• nonn

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

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

Crossrefs

Cf. A082730.

Programs

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

Extensions

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