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 A358320 #108 Nov 19 2022 19:20:06
%S A358320 12285,3,7,779,31,37,127,651,2927269,93,25329329,7230607,8191,
%T A358320 66445153,7613527,18431675687,131071,264003743,524287,59592560831,
%U A358320 949755039781
%N A358320 Least odd number m such that m*2^n is a perfect, amicable or sociable number, and -1 if no such number exists.
%C A358320 For n in {1,2,4,6,12,16,18}, a(n)*2^n is a perfect number. See A090748.
%C A358320 For n in {0,3,5,8,10,11,13,14,15,17,19}, a(n)*2^n is an amicable number.
%C A358320 For n in {7,9} a(n)*2^n is a sociable number of order 28.
%C A358320 That is, h_k(m*2^n) = m*2^n for some k > 0, where h_{k+1}(n) = h_k(h(n)) and h(n) = A001065(n), the sum of aliquot parts of n. - _Charles R Greathouse IV_, Nov 09 2022
%C A358320 Least m such that m*2^n is in A347770. - _Charles R Greathouse IV_, Nov 09 2022
%H A358320 BOINC, <a href="https://sech.me/boinc/Amicable/">Amicable Numbers</a>
%H A358320 HandWiki, <a href="https://handwiki.org/wiki/List_of_perfect_numbers">List of perfect numbers</a>
%H A358320 David Moews, <a href="http://djm.cc/sociable.txt">A list of currently known aliquot cycles of length greater than 2</a>
%e A358320 a(1) = 3, because 3 is an odd number and 3 * 2^1 = 6 is a perfect number, and no lesser number has this property.
%o A358320 (PARI)
%o A358320 sigmap(n)=if(n<=1, return(0)); sigma(n)-n
%o A358320 cycle(n,TT=28)=my(x=n,T=1); while(x>0&&T<=TT, x=sigmap(x); if(x==n, return(T)); T++)
%o A358320 a(n,TT=28)=my(p2n=2^n); forstep(m=1, +oo, 2, if(cycle(p2n*m,TT), return(m)))
%Y A358320 Cf. A347770, A000396, A001065, A002025, A259180, A262625.
%Y A358320 Cf. A090748, A358415.
%K A358320 nonn,more
%O A358320 0,1
%A A358320 _Jean-Marc Rebert_, Nov 09 2022
%E A358320 a(0), a(15)-a(20) from _Jean-Marc Rebert_, Nov 17 2022