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

2,5

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A065855, A000720, A073437.

Sequence in context: A330629 A304760 A304759 * A187096 A340146 A340143

Adjacent sequences: A073435 A073436 A073437 * A073439 A073440 A073441

Keyword

nonn

Author

Labos Elemer, Jul 31 2002

Status

approved