A211656 - OEIS

%I #32 Dec 20 2021 02:40:59

%S 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,

%T 72,73,81,91,98,100,101,106,109,121,128,129,133,134,137,146,148,149,

%U 152,157,162,163,169,171,173,192,193,197,199,200,202,211,217,218,219

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

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

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

%C 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).

%H Robert Israel, <a href="/A211656/b211656.txt">Table of n, a(n) for n = 1..10000</a>

%e 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).

%p N:= 1000: # to get terms < the least m with sigma(m) > N

%p S:= map(numtheory:-sigma, [$1..N-1]):

%p m:=min(select(t -> S[t]>N, [$1..N-1]))-1:

%p select(n->numboccur(S[n],S)=1, [$1..m]); # _Robert Israel_, Jul 04 2019

%t 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 *)

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

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Apr 20 2012