A161975 Sum_{x=sum of prime factors of n-th composite..n-th composite} x.

4, 11, 21, 30, 34, 57, 69, 92, 108, 143, 174, 186, 175, 264, 280, 246, 342, 351, 420, 483, 470, 424, 564, 621, 531, 660, 765, 837, 885, 980, 781, 1121, 1134, 1209, 1136, 1242, 1430, 1420, 1518, 1422, 1246, 1764, 1425, 1938, 2014, 1992, 2091, 2136, 2090, 2394

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 23 2009

Keywords

• nonn

Examples

			4(=4), 11(=(2+3)+6), 22(=(2+2+2)+7+8), 30(=(3+3)+7+9), 34(=(2+5)+8+9+10), etc.
		

Crossrefs

Cf. A002808.

Programs

Maple

A002808 := proc(n) option remember ; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end: A001414 := proc(n) pfs :=ifactors(n)[2] ; add(op(1,p)*op(2,p) ,p=pfs) ; end: A046343 := proc(n) A001414(A002808(n)); end: A000217 := proc(n) n*(n+1)/2 ; end: A161975 := proc(n) A000217( A002808(n)) - A000217(A046343(n)-1) ; end: seq(A161975(n),n=1..90) ; # R. J. Mathar, Aug 03 2009

PARI

a(n)=my(c=n+n\log(n+1),f);for(i=0,n-c+primepi(c),if(isprime(c++),i--));f=factor(c);binomial(c+1,2)-binomial(sum(i=1,#f[,1],f[i,1]*f[i,2]),2)

Extensions

a(3), a(12) and others corrected by R. J. Mathar, Aug 03 2009

Program by Charles R Greathouse IV, Oct 12 2009