login
A319917
Unitary sociable numbers of order six.
4
698130, 698310, 698490, 712710, 712890, 713070, 341354790, 348612390, 391662810, 406468314, 411838938, 519891750, 530946330, 582129630, 596171970, 621549630, 717175170, 740700270, 740700450, 743324934, 838902150, 919121658, 1009954170, 1343332998
OFFSET
1,1
COMMENTS
Note that the first 6 terms and the next 6 terms form two sociable groups. But then the next 12 terms belong to two distinct sociable groups.
LINKS
J. O. M. Pedersen, Known Unitary Sociable Numbers of order different from four [Via Internet Archive Wayback-Machine]
J. O. M. Pedersen, Order 6 cycles, 2007.
Eric Weisstein's World of Mathematics, Unitary Sociable Numbers
PROG
(PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;
isok6(n) = iferr(f(f(f(f(f(f(n)))))) == n, E, 0);
isok3(n) = iferr(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) = isok6(n) && !isok1(n) && !isok2(n) && !isok3(n);
(PARI)
A063919(n) = my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^f[i, 2] + 1) - n
is(n) = my(c = n); for(i = 1, 5, c = A063919(c); if(c == 1 || c == n, return(0))); c = A063919(c); c == n \\ David A. Corneth, Oct 01 2018
CROSSREFS
Cf. A063919 (sum of proper unitary divisors).
Cf. A002827 (unitary perfect), A063991 (unitary amicable).
Cf. A319902 (order 4), A097024 (order 5), A097030 (order 14).
Sequence in context: A346358 A206518 A114676 * A205608 A205439 A027829
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 01 2018
STATUS
approved