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

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, 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, 11, 12, 10, 11, 9, 10, 11, 12, 13, 14, 12, 13, 14, 15, 13, 14, 15, 16, 17, 18, 16, 17, 18

Offset: 2

Author

Labos Elemer, Jul 31 2002

Keywords

• nonn

Examples

			n=100: G[100]=100-Pi[100]-1=100-25-1=74, Pi[100]=25, remainder=a(100)=Mod[74,25]=24.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A065855, A000720, A073437.

Programs

Mathematica

Table[Mod[w-PrimePi[w]-1, PrimePi[w]], {w, 1, 128}]
With[{nn=100},Mod[#[[1]]-#[[2]]-1,#[[2]]]&/@Thread[{Range[2,nn],PrimePi[Range[2,nn]]}]] (* Harvey P. Dale, Feb 26 2025 *)

Formula

a(n)=Mod[A065855(n), A000720(n)]=Mod[n-Pi[n]-1, Pi[n]] for n>1.