A097704 Terms of A097703 that are not of the form 3*k + 1.

12, 24, 60, 62, 84, 87, 122, 137, 144, 162, 171, 180, 212, 237, 264, 269, 287, 302, 312, 318, 362, 387, 416, 420, 422, 423, 437, 462, 465, 480, 512, 537, 563, 587, 591, 612, 662, 665, 684, 687, 710, 722, 737, 759, 762, 786, 812, 837, 840, 857, 887, 902

Offset: 1

Author

Ralf Stephan, Aug 26 2004

Keywords

• nonn

Comments

Conjecture: "most" of the terms also belong to [(A067778-1)/2]. Exceptions are {302, 2117, ...} (A098241). In other words, most terms satisfy: GCD(2*k+1, numerator(B(4*k+2))) is not squarefree, with B(n) the Bernoulli numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A007494 and A097703.

Cf. A013929, A027641, A027642, A067778, A098241.

Programs

Mathematica

usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; Complement[ Range[1017], Table[3k - 2, {k, 340}], (Select[ Range[220000], DivisorSigma[1, # ] == 2usigma[ # ] &] - 108)/216] (* Robert G. Wilson v, Aug 28 2004 *)

PARI

is(k) = if(k % 3 == 1, 0, 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