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A327157 Numbers that are members of unitary sigma aliquot cycles (union of unitary perfect, unitary amicable and unitary sociable numbers). 3
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 (list; graph; refs; listen; history; text; internal format)
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.

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 * A309312 A101937 A101939

Adjacent sequences:  A327154 A327155 A327156 * A327158 A327159 A327160

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 17 2019

STATUS

approved

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Last modified December 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)