A163830 The n-th composite minus the product of the indices of the primes in its prime factorization.

3, 4, 7, 5, 7, 10, 10, 9, 15, 14, 17, 13, 17, 22, 16, 20, 19, 24, 24, 31, 23, 27, 23, 32, 30, 27, 37, 34, 39, 33, 37, 46, 33, 41, 37, 46, 46, 40, 52, 41, 48, 54, 51, 47, 63, 47, 56, 61, 51, 58, 68, 62, 57, 68, 57, 66, 77, 65, 69, 76, 64, 72, 67, 83, 78, 67, 83, 71, 79, 71, 94

Offset

1,1

Comments

The product of the indices of the primes (counted with multiplicity) is represented by A003963. An intermediate sequence m-A003963(m) = 0, 1, 1, 3, 2, 4, 3, 7, 5, 7, 6, ... at m=1, 2, 3, ... is defined and evaluated where m=A002808(n) is composite.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = A002808(n) - A003963(A002808(n)).

Example

At n=1, A002808(1) = 4 and A003963(4)=1, so a(1) = 4 - 1 = 3.
At n=2, A002808(2) = 6 and A003963(6)=2, so a(2) = 6 - 2 = 4.
At n=3, A002808(3) = 8 and A003963(8)=1, so a(3) = 8 - 1 = 7.

Maple

A002808 := proc(n) local a; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; end if; end do; end if; end proc:
A163829 := proc(n) local c; c := A002808(n) ; pfs := ifactors(c)[2] ; mul( numtheory[pi](op(1, p))^op(2, p), p=pfs) ; end:
A163830 := proc(n) A002808(n)-A163829(n) ; end: seq(A163830(n), n=1..100) ; # R. J. Mathar, Aug 08 2009

Mathematica

With[{nn=100}, #-Times@@(PrimePi/@Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[#]])&/@Complement[Range[2, nn], Prime[Range[ PrimePi[ nn]]]]](* Harvey P. Dale, Mar 29 2012 *)

Crossrefs

Cf. A002808, A163515, A003963.

Sequence in context: A267447 A071051 A212807 * A254931 A338285 A050197

Adjacent sequences: A163827 A163828 A163829 * A163831 A163832 A163833

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 05 2009

Extensions

Edited by R. J. Mathar, Jul 08 2009

Status

approved