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.

A081305 Number of numbers m <= n with at least one prime factor greater than 2*spf(m), where spf(m) is the smallest prime factor of m (A020639).

This page as a plain text file.
%I A081305 #8 Jul 27 2020 15:52:13
%S A081305 0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,3,4,5,5,5,5,6,6,7,7,8,8,8,9,10,
%T A081305 10,10,10,11,12,13,13,14,14,15,15,16,16,16,16,17,18,19,19,19,20,21,22,
%U A081305 23,23,24,24,25,26,26,27,28,28,29,30,31,31,31,31,32,32,33,33,34,34,35
%N A081305 Number of numbers m <= n with at least one prime factor greater than 2*spf(m), where spf(m) is the smallest prime factor of m (A020639).
%C A081305 a(n)+A081304(n)=n; a(114)=A081304(114)=57;
%C A081305 a(n)<=n/2 for n<=114, a(n)>n/2 for n>114.
%H A081305 Robert Israel, <a href="/A081305/b081305.txt">Table of n, a(n) for n = 1..10000</a>
%p A081305 f:= proc(n) local R; R:= numtheory:-factorset(n); if max(R) > 2*min(R) then 1 else 0 fi end proc:
%p A081305 ListTools:-PartialSums(map(f, [$1..100])); # _Robert Israel_, Jul 27 2020
%t A081305 pfg[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},If[Last[f]> 2*First[ f], 1,0]]; Accumulate[Array[pfg,80]] (* _Harvey P. Dale_, Apr 28 2014 *)
%Y A081305 Cf. A069900, A081303.
%K A081305 nonn
%O A081305 1,14
%A A081305 _Reinhard Zumkeller_, Mar 17 2003