This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345058 #13 Jan 26 2022 08:28:47
%S A345058 1,2,1,3,2,2,2,7,4,2,2,4,4,3,1,5,4,4,3,7,2,3,2,7,6,4,3,3,4,7,4,13,3,4,
%T A345058 2,4,6,3,4,7,6,3,4,7,1,5,2,7,11,6,2,7,4,5,2,11,3,4,2,7,8,5,5,7,2,3,4,
%U A345058 4,5,3,4,13,9,6,6,9,2,4,4,8,15,6,2,11,3,3,3,7,6,3,1,5,4,7,3,13,10,11,7,6,6,5,4,8,2
%N A345058 Number of distinct k > 0 for which A011772(k) = n.
%C A345058 Question: Are there any numbers n other than 1, 3, 15, 45, 91 for which a(n) = 1?
%F A345058 a(n) = Sum_{i=1..A000217(n)} [A011772(i) = A011772(n)], where [ ] is the Iverson bracket.
%e A345058 A011772 obtains the value 6 only as A011772(7)=6 and A011772(36)=6, therefore a(6) = 2.
%o A345058 (PARI)
%o A345058 A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
%o A345058 A345058(n) = { my(x=A011772(n), y=binomial(x+1,2)); sum(i=1,y,(A011772(i)==x)); };
%Y A345058 Cf. A000217, A002024, A011772, A066561, A345056, A345057.
%K A345058 nonn
%O A345058 1,2
%A A345058 _Antti Karttunen_, Jun 07 2021