|
| |
|
|
A073040
|
|
Numbers n such that sum of divisors of n, sigma (n), minus n is a square.
|
|
4
| |
|
|
1, 2, 3, 5, 7, 9, 11, 12, 13, 15, 17, 19, 23, 24, 26, 29, 31, 37, 41, 43, 47, 53, 56, 59, 61, 67, 71, 73, 75, 76, 79, 83, 89, 90, 95, 97, 101, 103, 107, 109, 113, 119, 122, 124, 127, 131, 137, 139, 140, 143, 147, 149, 151, 153, 157, 163, 167, 173, 176, 179, 181, 191
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
FORMULA
| {n: A001065(n) in A000290} - R. J. Mathar, Dec 11 2010
|
|
|
EXAMPLE
| a(6) = 9 because the divisors of 9 are 1, 3, 9, and (1+3+9)-9 = 4 = 2^2.
The number 10 is not in the sequence because (1+2+5+10)-10 = 8, which is not a square.
a(7) = 11 because (1+11)-11 = 1, a square.
|
|
|
MAPLE
| with(numtheory); a := []; for n from 1 to 2000 do if issqr(sigma(n)-n) then a := [op(a), n]; fi; od: a;
|
|
|
MATHEMATICA
| Select[Range[200], IntegerQ[Sqrt[-# + Plus@@Divisors[#]]] &] (* From Alonso del Arte, Dec 08 2010 *)
|
|
|
CROSSREFS
| Cf. A048698, which excludes primes.
Sequence in context: A155498 A069149 A042996 * A087268 A106765 A190785
Adjacent sequences: A073037 A073038 A073039 * A073041 A073042 A073043
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 24 2002
|
| |
|
|
