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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). 3

%I #8 Jul 27 2020 15:52:13

%S 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 10,10,10,11,12,13,13,14,14,15,15,16,16,16,16,17,18,19,19,19,20,21,22,

%U 23,23,24,24,25,26,26,27,28,28,29,30,31,31,31,31,32,32,33,33,34,34,35

%N 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 a(n)+A081304(n)=n; a(114)=A081304(114)=57;

%C a(n)<=n/2 for n<=114, a(n)>n/2 for n>114.

%H Robert Israel, <a href="/A081305/b081305.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local R; R:= numtheory:-factorset(n); if max(R) > 2*min(R) then 1 else 0 fi end proc:

%p ListTools:-PartialSums(map(f, [$1..100])); # _Robert Israel_, Jul 27 2020

%t 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 Cf. A069900, A081303.

%K nonn

%O 1,14

%A _Reinhard Zumkeller_, Mar 17 2003

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Last modified April 25 09:15 EDT 2024. Contains 371967 sequences. (Running on oeis4.)