A088005 Numbers whose abundance is (+-1) times a prime.

3, 9, 10, 18, 20, 25, 36, 49, 50, 81, 100, 104, 121, 136, 196, 225, 289, 324, 338, 392, 464, 484, 576, 650, 676, 784, 800, 841, 900, 961, 968, 1058, 1089, 1156, 1225, 1250, 1352, 1682, 1936, 1952, 2209, 2312, 2450, 2500, 2888, 3136, 3364, 3721, 4225, 4356

Offset: 1

Author

Labos Elemer, Oct 18 2003

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000203, A000040, A077374, A087998.

Programs

Mathematica

ab[x_] := DivisorSigma[1, x]-2*x Do[If[PrimeQ[s=ab[n]], Print[{n, s}]], {n, 1, 10000}]

PARI

isok(n) = isprime(abs(sigma(n)-2*n)); \\ Michel Marcus, Sep 21 2019

Formula

abs(sigma(n)-2n) is a prime.