login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A163830 The n-th composite minus the product of the indices of the primes in its prime factorization. 1
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 (list; graph; refs; listen; history; text; internal format)
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. A000040, A002909, A163515, A003963.

Sequence in context: A109823 A071051 A212807 * A050197 A003975 A082226

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 21 08:32 EST 2014. Contains 252299 sequences.