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.

A073438 Remainder of division G[n]/Pi[n], where G[n] is the number of composites not exceeding n.

This page as a plain text file.
%I A073438 #11 Feb 26 2025 15:35:31
%S A073438 0,0,1,1,2,2,3,0,1,0,1,0,1,2,3,2,3,2,3,4,5,4,5,6,7,8,0,8,9,8,9,10,0,1,
%T A073438 2,0,1,2,3,1,2,0,1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,6,7,8,9,10,11,9,10,
%U A073438 11,12,10,11,9,10,11,12,13,14,12,13,14,15,13,14,15,16,17,18,16,17,18
%N A073438 Remainder of division G[n]/Pi[n], where G[n] is the number of composites not exceeding n.
%H A073438 Harvey P. Dale, <a href="/A073438/b073438.txt">Table of n, a(n) for n = 2..1000</a>
%F A073438 a(n)=Mod[A065855(n), A000720(n)]=Mod[n-Pi[n]-1, Pi[n]] for n>1.
%e A073438 n=100: G[100]=100-Pi[100]-1=100-25-1=74, Pi[100]=25, remainder=a(100)=Mod[74,25]=24.
%t A073438 Table[Mod[w-PrimePi[w]-1, PrimePi[w]], {w, 1, 128}]
%t A073438 With[{nn=100},Mod[#[[1]]-#[[2]]-1,#[[2]]]&/@Thread[{Range[2,nn],PrimePi[Range[2,nn]]}]] (* _Harvey P. Dale_, Feb 26 2025 *)
%Y A073438 Cf. A065855, A000720, A073437.
%K A073438 nonn
%O A073438 2,5
%A A073438 _Labos Elemer_, Jul 31 2002