A266874 Excess of the odd abundant numbers that are congruent to 1 mod 4 over those that are congruent to 3 mod 4.

1, 0, 1, 0, 1, 0, 1, 0, -1, 0, -1, -2, -1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 0, -1, 0, -1, 0, -1, -2, -3, -2, -3, -2, -3, -4, -3, -4, -3, -2, -1, -2, -1, 0

Offset

1,12

Comments

Pollack and Kobayashi ask if a(n) can be arbitrarily large and if 0 can appear infinitely often (see Slide 21 in the links).

Links

Table of n, a(n) for n=1..86.

Paul Pollack and Mits Kobayashi, The distribution of abundant numbers, Slides, Integers Conference 2013: Erdős Centennial, University of Georgia, October 24, 2013.

Mathematica

Reap[For[nbe = 0; n = 1, n < 10^5, n += 2, If[DivisorSigma[1, n] > 2*n, If[Mod[n, 4] == 1, nbe++, nbe--]; Sow[nbe]]]][[2, 1]] (* Jean-François Alcover, Jan 05 2016, adapted from PARI *)

Prog

(PARI) lista(nn) = {nbe = 0; forstep(n=1, nn, 2, if (sigma(n) > 2*n, if (n % 4 == 1, nbe++, nbe--); print1(nbe, ", "); ); ); }

Crossrefs

Cf. A005231.

Sequence in context: A227573 A085004 A095774 * A308343 A331216 A071993

Adjacent sequences: A266871 A266872 A266873 * A266875 A266876 A266877

Keyword

sign

Author

Michel Marcus, Jan 05 2016

Status

approved