A211656 Numbers n such that value of sigma(n) is unique; sigma(n) = A000203(n) = sum of divisors of n.

1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 18, 19, 22, 27, 29, 32, 36, 37, 43, 45, 49, 50, 61, 64, 67, 72, 73, 81, 91, 98, 100, 101, 106, 109, 121, 128, 129, 133, 134, 137, 146, 148, 149, 152, 157, 162, 163, 169, 171, 173, 192, 193, 197, 199, 200, 202, 211, 217, 218, 219

Offset

1,2

Comments

Values of sigma(n) in increasing order are in A007370. Corresponding values of sigma(a(n)) is in A211657(n).

Complement of A206036 (numbers n such that sigma(n) = sigma(k) has solution for distinct numbers n and k).

Union of A066076 (primes p such that value of sigma(p) is unique) and A211658 (nonprimes p such that value of sigma(p) is unique).

Links

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

Example

Number 36 is in sequence because sigma(36) = 91 and there is no other number m with sigma(m) = 91. Number 6 is not in the sequence because sigma(6) = 12 and 12 is also sigma(11).

Maple

N:= 1000: # to get terms < the least m with sigma(m) > N
S:= map(numtheory:-sigma, [$1..N-1]):
m:=min(select(t -> S[t]>N, [$1..N-1]))-1:
select(n->numboccur(S[n], S)=1, [$1..m]); # Robert Israel, Jul 04 2019

Mathematica

nn = 300; mx = Max[DivisorSigma[1, Range[nn]]]; d = DivisorSigma[1, Range[mx]]; t = Transpose[Select[Sort[Tally[d]], #[[1]] <= mx && #[[2]] == 1 &]][[1]]; Select[Range[nn], MemberQ[t, d[[#]]] &] (* T. D. Noe, Apr 20 2012 *)

Crossrefs

Cf. A000203, A007370, A066076, A211657, A211658, A211659, A211660, A206036.

Sequence in context: A160519 A287927 A241480 * A051204 A335154 A278181

Adjacent sequences: A211653 A211654 A211655 * A211657 A211658 A211659

Keyword

nonn

Author

Jaroslav Krizek, Apr 20 2012

Status

approved