cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A303736 Number of deficient numbers < 10^n.

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%I A303736 #17 Jul 02 2022 16:14:00
%S A303736 8,76,751,7508,75201,752451,7523259,75239327,752389040,7523761073,
%T A303736 75238050781,752382051546,7523801085404,75237991990847,
%U A303736 752380354682456,7523805396029055,75238037557271886
%N A303736 Number of deficient numbers < 10^n.
%C A303736 Limit_{n->oo} a(n)/10^n = 0.752... is the density of deficient numbers (A005100).
%t A303736 Accumulate@ Array[Count[Range[10^#, 10^(# + 1) - 1], _?(DivisorSigma[1, #] < 2 # &)] &, 6, 0] (* _Michael De Vlieger_, May 20 2018 *)
%o A303736 (GAP) P:=Filtered([1..10^7],n->Sigma(n)<2*n);;
%o A303736 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;
%o A303736 a:=List(o,Length);
%o A303736 (PARI) a(n) = sum(k=1, 10^n-1, sigma(k) < 2*k); \\ _Michel Marcus_, May 19 2018
%Y A303736 Cf. A005100, A302992.
%K A303736 nonn,more
%O A303736 1,1
%A A303736 _Muniru A Asiru_, May 19 2018
%E A303736 a(11)-a(17) from _Hiroaki Yamanouchi_, Aug 03 2018