1,1

Numbers k such that n = 216k+108 satisfies sigma(n) <> 2*usigma(n) (A097703), n not of form 3x+1 (A007494), and GCD(2n+1, numerator(Bernoulli(4n+2))) squarefree (A098240).

Also, members n of A097704 such that GCD(2n+1, Bernoulli(4n+2)) is squarefree. Most terms of A097704 are in A098240. These are the exceptions.

(* first *) Needs["NumberTheory`NumberTheoryFunctions`"] (* then *) usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; lmt = 1296000; t = (Select[ Range[ lmt], DivisorSigma[1, # ] == 2usigma[ # ] &] - 108)/216; u = (Select[ Range[ Floor[(lmt - 108)/432]], !SquareFreeQ[ GCD[ #, Numerator[ BernoulliB[ 2# ]] ]] &] -1)/2; v = Table[ 3k - 2, {k, Floor[(lmt - 108)/216]}]; Complement[ Range[ Floor[ (lmt - 108)/216]], t, u, v]

Cf. A016777, A063880, A067778.

Sequence in context: A068258 A075407 A004227 this_sequence A058828 A005951 A030030

Adjacent sequences: A098238 A098239 A098240 this_sequence A098242 A098243 A098244

nonn,more

Ralf Stephan (ralf(AT)ark.in-berlin.de) and Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 15 2004