OFFSET
1,1
COMMENTS
The sequence includes all numbers of the form 6 * p^2 with p a prime >= 5. All of the terms above are of this form, except for 1428. There are similar subsequences corresponding to each of the five known unitary perfect numbers (A002827), namely 60 * p^9 (p>=7), 90 * p^14 (p>=7), 87360 * p^1559 (p=11 or p>=17) and 146361946186458562560000 * p^3009086064688703999 (p>=17 and not equal to 19, 37, 79, 109, 157, or 313). It is not known if there are other terms in the sequence besides these and 1428. - Dean Hickerson
The term 33872160 was found later: it is not of the form a * p^e where a is a unitary perfect number and p is a prime not dividing a. - Jason Earls
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..5000
MATHEMATICA
usigma[n_] := Sum[d*Boole[GCD[d, n/d] == 1], {d, Divisors[n]}]; Reap[For[n = 1, n < 140000, n++, If[usigma[n] == 2 n + DivisorSigma[0, n], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jan 16 2013 *)
PROG
(PARI) us(n)=sumdiv(n, d, if(gcd(d, n/d)==1, d));
for(n=1, 10^8, if(us(n)==2*n+numdiv(n), print1(n, ", ")))
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Jason Earls, Aug 20 2001
STATUS
approved