A161517 Sum of remainders of c mod k where k = 1, 2, 3, ..., c and c is the n-th composite number.

1, 3, 8, 12, 13, 17, 31, 36, 36, 47, 61, 70, 77, 85, 103, 112, 125, 124, 138, 167, 184, 197, 218, 198, 248, 269, 258, 284, 328, 339, 358, 374, 414, 420, 449, 454, 492, 529, 520, 553, 578, 586, 672, 693, 693, 738, 725, 799, 840, 835, 852, 956, 981, 992, 1049, 1036

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 12 2009

Keywords

• nonn
• easy

Examples

			a(1) = 1 (= (4 mod 3) + 0);
a(2) = 3 (= (6 mod 5) + (6 mod 4) + 0 + 0);
a(3) = 8 (= (8 mod 7) + (8 mod 6) + (8 mod 5) + 0 + (8 mod 3) + 0), etc.
		

Links

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

Crossrefs

Cf. A002808, A004125.

Programs

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: A004125 := proc(n) add( n mod k, k=1..n) ; end: A161517 := proc(n) local c; A004125( A002808(n)) ; end: seq(A161517(n),n=1..80) ; # R. J. Mathar, Aug 03 2009

Mathematica

With[{cmps=Select[Range[200],CompositeQ]},Table[Total[Mod[n,Range[n-1]]],{n,cmps}]] (* Harvey P. Dale, Apr 09 2023 *)

PARI

a(n)=my(c=n+n\log(n+1));for(i=0,n-c+primepi(c),if(isprime(c++),i--));sum(k=2,c,c%k) \\ Charles R Greathouse IV, Oct 12 2009

Formula

a(n) = (c mod (c-1)) + (c mod (c-2)) + ... + (c mod 3) + (c mod 2).

Extensions

Corrected and extended by R. J. Mathar, Aug 03 2009