OFFSET
1,2
COMMENTS
Conjecture: k is a term iff 6*k+3 is squarefree. - Vladeta Jovovic, Aug 27 2004
It is only a conjecture that all terms are integers (confirmed up to 10^6 by Robert G. Wilson v).
From Amiram Eldar, Aug 31 2024: (Start)
The first conjecture is true. If m = 216*k + 108 = 108 * (2*k + 1) is a term of A063880, then 2*k+1 is a squarefree number coprime to 6. This is because sigma(n)/usigma(n) is multiplicative, equals 1 if and only if n is squarefree and larger than 1 otherwise, sigma(108)/usigma(108) = 2 and sigma(3^k)/usigma(3^k) increases with k. 6*k+3 = 3*(2*k+1) is squarefree because 2*k+1 is a squarefree coprime to 6.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; (Select[ Range[ 24500], DivisorSigma[1, # ] == 2usigma[ # ] &] - 108)/216 (* Robert G. Wilson v, Aug 28 2004 *)
PROG
(PARI) {u(n)=sumdiv(n, d, if(gcd(d, n/d)==1, d))}
n=2; while(n<50000, n++; if(sigma(n)==2*u(n), print1((n-108)/216", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Aug 26 2004
STATUS
approved