OFFSET
1,2
COMMENTS
Conjecture: all numbers of form 3k + 1 are here. Other terms are listed in A097704.
From Amiram Eldar, Aug 31 2024: (Start)
The conjecture is true. If j = 3*k+1, then m = 324*(2*k+1). Let e = A007949(2*k+1) >= 0, so 2*k+1 = 3^e * i and i coprime to 6. Then sigma(m)/(2 * usigma(m)) = (7/20) * (3^(e+5)-1)/(3^(e+4)+1) * sigma(i)/usigma(i) >= 847/820 > 1, because sigma(i)/usigma(i) >= 1 for all i.
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 &]]; Complement[ Range[157], (Select[ Range[37000], DivisorSigma[1, # ] == 2usigma[ # ] &] - 108)/216] (* Robert G. Wilson v, Aug 28 2004 *)
PROG
(PARI) is(k) = {my(f = factor(216*k + 108)); sigma(f) != 2 * prod(i = 1, #f~, 1 + f[i, 1]^f[i, 2]); } \\ Amiram Eldar, Aug 31 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Aug 26 2004
STATUS
approved