A319917 Unitary sociable numbers of order six.

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

Table of n, a(n) for n=1..24.

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

Adjacent sequences: A319914 A319915 A319916 * A319918 A319919 A319920

Keyword

nonn

Author

Michel Marcus, Oct 01 2018

Status

approved