A303736 Number of deficient numbers < 10^n.

8, 76, 751, 7508, 75201, 752451, 7523259, 75239327, 752389040, 7523761073, 75238050781, 752382051546, 7523801085404, 75237991990847, 752380354682456, 7523805396029055, 75238037557271886

Offset: 1

Author

Muniru A Asiru, May 19 2018

Keywords

• nonn
• more

Comments

Limit_{n->oo} a(n)/10^n = 0.752... is the density of deficient numbers (A005100).

Crossrefs

Cf. A005100, A302992.

Programs

GAP

P:=Filtered([1..10^7],n->Sigma(n)<2*n);;
o:=List([1..7],j->[]);; for i in [1..Length(P)] do for n in [1..Length(o)] do if P[i]<10^n then Add(o[n],P[i]); fi; od; od;
a:=List(o,Length);

Mathematica

Accumulate@ Array[Count[Range[10^#, 10^(# + 1) - 1], ?(DivisorSigma[1, #] < 2 # &)] &, 6, 0] (* _Michael De Vlieger, May 20 2018 *)

PARI

a(n) = sum(k=1, 10^n-1, sigma(k) < 2*k); \\ Michel Marcus, May 19 2018

Extensions

a(11)-a(17) from Hiroaki Yamanouchi, Aug 03 2018