A063880 Numbers k such that sigma(k) = 2*usigma(k).

108, 540, 756, 1188, 1404, 1836, 2052, 2484, 3132, 3348, 3780, 3996, 4428, 4644, 5076, 5724, 5940, 6372, 6588, 7020, 7236, 7668, 7884, 8316, 8532, 8964, 9180, 9612, 9828, 10260, 10476, 10908, 11124, 11556, 11772, 12204, 12420, 12852, 13716, 14148

Offset: 1

Author

Jason Earls, Aug 27 2001

Keywords

• easy
• nonn

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)

Crossrefs

Cf. A000203, A001694, A034448, A048146, A097702, A276378.

Programs

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 *)

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