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

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A005382, A007369.

Programs

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 ] ]

PARI

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