A060658 Even numbers n such that sigma(x) = n has no solution.

2, 10, 16, 22, 26, 34, 46, 50, 52, 58, 64, 66, 70, 76, 82, 86, 88, 92, 94, 100, 106, 116, 118, 122, 130, 134, 136, 142, 146, 148, 154, 166, 170, 172, 178, 184, 188, 190, 196, 202, 206, 208, 214, 218, 220, 226, 232, 236, 238, 244, 246, 250, 254, 262, 268, 274

Offset

1,1

Comments

Contains 2*p if p is a prime not in A005382. - Robert Israel, Sep 30 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(2) = 10 because there is no x < 10 whose sigma(x) = 10, an even number.

Maple

N:= 1000: # to get all terms <= N
V:= Vector(N):
for x from 1 to N-1 do
  v:= numtheory:-sigma(x);
  if v <= N then V[v]:= 1 fi
od:
select(t -> V[t]=0, [seq(i, i=2..N, 2)]); # Robert Israel, Sep 30 2018

Mathematica

a = {}; Do[ s = DivisorSigma[ 1, n ]; If[ EvenQ[ s ], a = Append[ a, s ] ], {n, 1, 400} ]; Complement[ Table[ 2n, {n, 1, 200} ], Union[ a ] ]

Prog

(PARI) isok(n) = !(n%2) && !sum(k=1, n, sigma(k)==n); \\ Michel Marcus, Mar 08 2017

Crossrefs

Cf. A005382, A007369.

Sequence in context: A138632 A175957 A307055 * A239321 A054028 A063716

Adjacent sequences: A060655 A060656 A060657 * A060659 A060660 A060661

Keyword

nonn

Author

Robert G. Wilson v, Apr 18 2001

Status

approved