A307961 The number of coreful perfect numbers (A307958) below 10^n.

0, 1, 9, 94, 940, 9359, 93611, 936098, 9361056, 93610484, 936104756, 9361047434

Offset: 1

Author

Amiram Eldar, May 08 2019

Keywords

• nonn
• more

Crossrefs

Cf. A307822, A307958, A307960.

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={}; 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, were c = 0.009361... is the asymptotic density of the coreful perfect numbers (A307960).

Extensions

a(11)-a(12) from Amiram Eldar, Jul 25 2025