A088006 Abundance values which are +1 or -1 times a prime.

-2, -5, -2, 3, 2, -19, 19, -41, -7, -41, 17, 2, -109, -2, 7, -47, -271, 199, -127, 71, 2, -37, 499, 2, -71, 199, 353, -811, 1021, -929, 59, -457, -449, -163, -683, -157, 41, -751, 251, 2, -2161, -19, 401, 467, -61, 967, -631, -3659, -2777, 3391, -4421, 269, -2333, -1201, -4969, 4999, -1103, -2647, -1097, 269

Offset

1,1

Links

Table of n, a(n) for n=1..60.

Formula

Solutions x to sigma[n]-2n=x where Abs[x] is a prime number.

Example

n=18: sigma[18]=18+9+6+3+2+1=39, 2n=36, abundance=3, a prime;
n=25: sigma[25]=25+5+1=31, 2n=50, abundance=-19.

Mathematica

ab[x_] := DivisorSigma[1, x]-2*x Do[If[PrimeQ[s=ab[n]], Print[s]], {n, 1, 10000}]
Select[Table[DivisorSigma[1, n]-2n, {n, 7000}], PrimeQ[Abs[#]]&] (* Harvey P. Dale, Aug 21 2011 *)

Crossrefs

Cf. A000203, A000040, A077374, A087998, A088005.

Sequence in context: A300691 A102707 A134486 * A078311 A132743 A192885

Adjacent sequences: A088003 A088004 A088005 * A088007 A088008 A088009

Keyword

sign

Author

Labos Elemer, Oct 18 2003

Status

approved