A308054 The number of coreful abundant numbers (A308053) below 10^n.

0, 1, 24, 259, 2614, 26222, 262220, 2622178, 26221610, 262215860, 2622158194

Offset: 1

Author

Amiram Eldar, May 10 2019

Keywords

• nonn
• more

Examples

			Below 10^2 there is only one coreful abundant number, 72, hence a(2) = 1.
		

Crossrefs

Cf. A302992, A302993, A302994, A307820, A307821, A307823, A307961, A308053.

Programs

Mathematica

f[p_, e_] := (p^(e+1)-1)/(p-1)-1; csigma[1]=1; csigma[n_] := Times @@ (f @@@ FactorInteger[n]); cpQ[n_] := csigma[n] > 2*n; s={0}; c=0; p=100; Do[If[k==p, AppendTo[s, c]; p*=10]; If[cpQ[k], c++], {k, 1, 1000001}]; s

Formula

a(n) ~ c * 10^n, where c = 0.0262215... is the asymptotic density of the coreful abundant numbers (see A308053). [Updated by Amiram Eldar, Sep 02 2022]

Extensions

a(11) from Amiram Eldar, Sep 02 2022