A096848 Primes arising in A096847.

2, 5, 17, 233, 683, 769, 4013, 5039, 28649, 29663, 24917, 15173, 24179, 105509, 252971, 81083, 871289, 941429, 639701, 199193, 713681, 768389, 873569, 1300813, 1308299, 1019687, 4459667, 1477139, 642779, 3953591, 2040443, 8445707, 4906973

Offset

1,1

Comments

Primes of the form m*tau(m) - sigma(m), listed in the order in which the values of m appear in A096847.

Links

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

Formula

a(n) = A094471(A096847(n)).

Mathematica

Do[s=n*DivisorSigma[0, n]-DivisorSigma[1, n]; If[PrimeQ[s], Print[{n, s}]; ta[[u]]=n; tb[[u]]=s; u=u+1], {n, 1, 1000000}]; ta
s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; n * Times @@ (e + 1) - Times @@ ((p^(e + 1) - 1)/(p - 1))]; q[n_] := PrimeQ[s[n]]; seq[lim_] := Module[{m1 = Floor[Sqrt[lim/2]], m2 = Floor[Sqrt[lim]/2]}, s /@ Join[{3}, Union[Select[2*Range[m1]^2, q], Select[4*Range[m2]^2, q]]]]; seq[200000] (* Amiram Eldar, Feb 14 2025 *)

Crossrefs

Cf. A000005 (tau), A000203 (sigma), A094471, A096847.

Sequence in context: A123374 A067339 A309178 * A283107 A269834 A290200

Adjacent sequences: A096845 A096846 A096847 * A096849 A096850 A096851

Keyword

nonn

Author

Labos Elemer, Jul 15 2004

Status

approved