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).

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, 10, 10, 10, 11, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17, 18, 19, 19, 19, 20, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 31, 31, 32, 32, 33, 33, 34, 34, 35

Offset: 1

Author

Reinhard Zumkeller, Mar 17 2003

Keywords

• nonn

Comments

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

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069900, A081303.

Programs

Maple

f:= proc(n) local R; R:= numtheory:-factorset(n); if max(R) > 2*min(R) then 1 else 0 fi end proc:
ListTools:-PartialSums(map(f, [$1..100])); # Robert Israel, Jul 27 2020

Mathematica

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 *)