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).
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 01 2018
STATUS
approved