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A098241 Numbers k such that n = 216k+108 is element of A097703 and A007494 and A098240. 0
302, 2117, 2909, 3327, 3932 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..5.

MATHEMATICA

(* 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]

CROSSREFS

Cf. A016777, A063880, A067778.

Sequence in context: A261677 A004227 A255144 * A252605 A252598 A252597

Adjacent sequences:  A098238 A098239 A098240 * A098242 A098243 A098244

KEYWORD

nonn,more

AUTHOR

Ralf Stephan and Robert G. Wilson v, Sep 15 2004

STATUS

approved

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Last modified January 19 20:22 EST 2022. Contains 350466 sequences. (Running on oeis4.)