A098241 - OEIS

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A098241

Numbers k such that 216*k+108 is a term of A097703 and A007494 and A098240.

302, 2117, 2909, 3327, 3932, 5142, 5747, 6957, 8772, 9377, 11192, 12402, 13007, 14217, 14547, 16032, 17847, 18452, 20267, 20366, 21477, 22082, 23292, 23897, 25107, 25403, 26922, 27527, 29342, 30552, 31157, 32367, 32972, 34182, 35997, 36602, 37823, 38417, 39627

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OFFSET

1,1

COMMENTS

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

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..100

MATHEMATICA

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]

q[n_] := Mod[n, 3] != 1 && (Divisible[2*n + 1, 3] || (! Divisible[2*n + 1, 3] && ! SquareFreeQ[2*n + 1])) && SquareFreeQ[GCD[2*n + 1, BernoulliB[4*n + 2]]]; Select[Range[10^4, q] (* Amiram Eldar, Aug 31 2024 *)

CROSSREFS

Cf. A000203, A034448, A007494, A016777, A027641, A027642, A063880, A067778, A097703, A097704, A098240.

Sequence in context: A261677 A004227 A255144 * A252605 A252598 A252597

Adjacent sequences: A098238 A098239 A098240 * A098242 A098243 A098244

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from Amiram Eldar, Aug 31 2024

STATUS

approved