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

6, 30, 42, 54, 60, 90, 114, 126, 1140, 1260, 1482, 1878, 1890, 2142, 2178, 2418, 2958, 3522, 3534, 3582, 3774, 3906, 3954, 3966, 3978, 4146, 4158, 4434, 4446, 18018, 22302, 24180, 29580, 32130, 35220, 35238, 35340, 35820, 37740, 38682, 39060, 39540, 39660, 39780, 40446, 41460, 41580, 44340, 44460, 44772, 45402

Offset

1,1

Comments

Positions of nonzeros in A327159.

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.

The terms that are not multiples of 6 are: 142310, 168730, 1077890, 1099390, 1156870, 1292570, ..., that seem all to be present in A063991.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..440

J. O. M. Pedersen, Known Unitary Sociable Numbers of order different from four [Via Internet Archive Wayback-Machine]

Example

6 is a member as A034460(6) = 6.
30 is a member as A034460(A034460(A034460(30))) = 30.

Mathematica

(* Function cycleL[] and support a034460[] are defined in A327159 *)
a327157[n_] := Map[cycleL, Range[n]]
a327157[45402] (* Hartmut F. W. Hoft, Feb 04 2024 *)

Prog

(PARI)
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); };
A034460(n) = (A034448(n) - n);
memo327159 = Map();
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)));
k=0; n=0; while(k<=1001, n++; if(t=A327159(n), k++; print(n, " -> ", t); write("b327157.txt", k, " ", n)));

Crossrefs

Cf. A002827, A063991, A097024, A097030, A319902, A319917, A319937 (subsequences), A034448, A034460, A097031, A327159.

Subsequence of A003062.

Sequence in context: A130512 A127662 A003062 * A336216 A309312 A101937

Adjacent sequences: A327154 A327155 A327156 * A327158 A327159 A327160

Keyword

nonn

Author

Antti Karttunen, Sep 17 2019

Status

approved