OFFSET
1,1
COMMENTS
Numbers so far are all == 108 (mod 216). - Ralf Stephan, Jul 07 2003 [Confirmed up to 10^7 by Robert G. Wilson v.]
Also numbers whose unitary and nonunitary divisors have equal sum. - Amiram Eldar, Sep 30 2019
From Amiram Eldar, Aug 31 2024: (Start)
The primitive terms of this sequence (terms whose proper divisors are not in this sequence) are all powerful numbers (A001694).
All the other terms are of the form m*s, where m is primitive (powerful) and s is a squarefree number coprime to m.
The only primitive term below 10^18 is 108.
If there are no other primitive terms, then a(n) = 108 * A276378(n). (End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
MATHEMATICA
usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; Select[ Range[14363], DivisorSigma[1, # ] == 2 usigma[ # ] &] (* Robert G. Wilson v, Aug 28 2004 *)
PROG
(PARI) u(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));
j=[]; for(n=1, 30000, if(sigma(n) == 2*u(n), j=concat(j, n))); j
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Aug 27 2001
STATUS
approved