A319902 - OEIS

A319902

Unitary sociable numbers of order 4.

263820, 263940, 280380, 280500, 395730, 395910, 420570, 420750, 172459210, 209524210, 218628662, 218725430, 230143790, 231439570, 246667790, 272130250, 384121920, 384296640, 408233280, 408408000

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OFFSET

1,1

COMMENTS

Is this a duplicate of A098188? - R. J. Mathar, Oct 04 2018

Note that the first 4 terms and the next 4 terms form two sociable groups. But then the next 8 terms belong to two distinct sociable groups, whereas in A098188 the integers are grouped by cycle.

From Hartmut F. W. Hoft, Aug 23 2023: (Start)

This sequence is A098188 in ascending order.

Among the 19 4-cycles listed in the link by J. O. M. Pedersen only four of the 6 possible patterns of relative sizes of the numbers in a cycle are realized. (End)

LINKS

Table of n, a(n) for n=1..20.

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

J. O. M. Pedersen, Order 4 cycles, 2007.

Eric Weisstein's World of Mathematics, Unitary Sociable Numbers

MATHEMATICA

f[n_] := f[n] = Module[{s = 0}, s = Total[Select[Divisors[n], GCD[#, n/#] == 1 &]]; Return[s - n]]; isok1[n_] := isok1[n] = Quiet[Check[f[n] == n, 0]]; isok2[n_] := isok2[n] = Quiet[Check[f[f[n]] == n, 0]]; isok4[n_] := isok4[n] = Quiet[Check[f[f[f[f[n]]]] == n, 0]]; isok[n_] := isok[n] = isok4[n] && Not[isok1[n]] && Not[isok2[n]]; Monitor[Position[Table[isok[n], {n, 1, 408408000}], True], n] (* Robert P. P. McKone, Aug 24 2023 *)

PROG

(PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;

isok4(n) = iferr(f(f(f(f(n)))) == n, E, 0);

isok2(n) = iferr(f(f(n)) == n, E, 0);

isok1(n) = iferr(f(n) == n, E, 0);

isok(n) = isok4(n) && !isok1(n) && !isok2(n);

CROSSREFS

Cf. A063919 (sum of proper unitary divisors).

Cf. A002827 (unitary perfect), A063991 (unitary amicable).

Cf. A097024 (order 5), A097030 (order 14).

Cf. A090615 (least member of sociable quadruples).

Cf. A098188.