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

1,2

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A002808, A004125.

Sequence in context: A361044 A288865 A331069 * A255199 A280239 A344345

Adjacent sequences: A161514 A161515 A161516 * A161518 A161519 A161520

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jun 12 2009

Extensions

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

Status

approved