A308054 - OEIS

%I #10 Sep 02 2022 04:58:59

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

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

%F 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]

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

%t 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

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

%K nonn,more

%O 1,3

%A _Amiram Eldar_, May 10 2019

%E a(11) from _Amiram Eldar_, Sep 02 2022