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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: A267447 A071051 A212807 * A254931 A050197 A003975

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

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Last modified December 5 21:40 EST 2016. Contains 278771 sequences.