cp's OEIS Frontend

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

%I A211656 #39 Jan 11 2025 03:12:22
%S A211656 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 A211656 72,73,81,91,98,100,101,106,109,121,128,129,133,134,137,146,148,149,
%U A211656 152,157,162,163,169,171,173,192,193,197,199,200,202,211,217,218,219
%N A211656 Numbers k such that the value of sigma(k) is unique; sigma(k) = A000203(k) = sum of divisors of k.
%C A211656 Values of sigma(n) in increasing order are in A007370. Corresponding values of sigma(a(n)) is in A211657(n).
%C A211656 Complement of A206036 (numbers n such that sigma(n) = sigma(k) has solution for distinct numbers n and k).
%C A211656 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 A211656 Robert Israel, <a href="/A211656/b211656.txt">Table of n, a(n) for n = 1..10000</a>
%H A211656 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A211656 Number 36 is in sequence because sigma(36) = 91 and there is no other number m with sigma(m) = 91.
%e A211656 Number 6 is not in the sequence because sigma(6) = 12 and 12 is also sigma(11).
%p A211656 N:= 1000: # to get terms < the least m with sigma(m) > N
%p A211656 S:= map(numtheory:-sigma, [$1..N-1]):
%p A211656 m:=min(select(t -> S[t]>N, [$1..N-1]))-1:
%p A211656 select(n->numboccur(S[n],S)=1, [$1..m]); # _Robert Israel_, Jul 04 2019
%t A211656 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 *)
%o A211656 (PARI) isok(k) = invsigmaNum(sigma(k)) == 1; \\ _Amiram Eldar_, Jan 11 2025, using _Max Alekseyev_'s invphi.gp
%Y A211656 Cf. A000203, A007370, A066076, A211657, A211658, A211659, A211660, A206036.
%K A211656 nonn
%O A211656 1,2
%A A211656 _Jaroslav Krizek_, Apr 20 2012