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A327157 Numbers that are members of unitary sigma aliquot cycles (union of unitary perfect, unitary amicable and unitary sociable numbers).

%I A327157 #29 Feb 04 2024 18:26:49
%S A327157 6,30,42,54,60,90,114,126,1140,1260,1482,1878,1890,2142,2178,2418,
%T A327157 2958,3522,3534,3582,3774,3906,3954,3966,3978,4146,4158,4434,4446,
%U A327157 18018,22302,24180,29580,32130,35220,35238,35340,35820,37740,38682,39060,39540,39660,39780,40446,41460,41580,44340,44460,44772,45402
%N A327157 Numbers that are members of unitary sigma aliquot cycles (union of unitary perfect, unitary amicable and unitary sociable numbers).
%C A327157 Positions of nonzeros in A327159.
%C A327157 Numbers n for which n = A034460^k(n) for some k >= 1, where A034460^k(n) means k-fold application of A034460 starting from n.
%C A327157 The terms that are not multiples of 6 are: 142310, 168730, 1077890, 1099390, 1156870, 1292570, ..., that seem all to be present in A063991.
%C A327157 Among the first 440 terms, there are numbers present in 1-cycles (A002827), 2-cycles (A063991), and also cycles of sizes 3, 4 (A319902), 5 (A097024), 6 (A319917), 14 (A097030), 25, 26, 39 and 65.
%H A327157 Antti Karttunen, <a href="/A327157/b327157.txt">Table of n, a(n) for n = 1..440</a>
%H A327157 J. O. M. Pedersen, <a href="http://web.archive.org/web/20130731050921/http://amicable.homepage.dk/knwnux.htm">Known Unitary Sociable Numbers of order different from four</a> [Via Internet Archive Wayback-Machine]
%e A327157 6 is a member as A034460(6) = 6.
%e A327157 30 is a member as A034460(A034460(A034460(30))) = 30.
%t A327157 (* Function cycleL[] and support a034460[] are defined in A327159 *)
%t A327157 a327157[n_] := Map[cycleL, Range[n]]
%t A327157 a327157[45402] (* _Hartmut F. W. Hoft_, Feb 04 2024 *)
%o A327157 (PARI)
%o A327157 A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); };
%o A327157 A034460(n) = (A034448(n) - n);
%o A327157 memo327159 = Map();
%o A327157 A327159(n) = if(1==n,0,my(v,orgn=n,xs=Set([])); if(mapisdefined(memo327159, n, &v), v, while(n && !vecsearch(xs,n), xs = setunion([n],xs); n = A034460(n); if(mapisdefined(memo327159,n),for(i=1,#xs,mapput(memo327159,xs[i],0)); return(0))); if(n==orgn,v = length(xs); for(i=1,v,mapput(memo327159,xs[i],v)), v = 0; mapput(memo327159,orgn,v)); (v)));
%o A327157 k=0; n=0; while(k<=1001, n++; if(t=A327159(n), k++; print(n," -> ",t); write("b327157.txt", k," ", n)));
%Y A327157 Cf. A002827, A063991, A097024, A097030, A319902, A319917, A319937 (subsequences), A034448, A034460, A097031, A327159.
%Y A327157 Subsequence of A003062.
%K A327157 nonn
%O A327157 1,1
%A A327157 _Antti Karttunen_, Sep 17 2019