A162733 Sum of remainders of the n-th composite mod k, for k=1,2,3,...,n.

0, 0, 2, 2, 3, 2, 10, 15, 15, 19, 25, 34, 41, 40, 58, 67, 80, 79, 83, 101, 118, 131, 152, 132, 170, 191, 180, 193, 223, 234, 253, 254, 294, 300, 329, 334, 356, 393, 384, 417, 442, 433, 501, 522, 522, 567, 554, 609, 650, 645, 642, 725, 750, 761, 818, 805, 833, 873

Offset

1,3

Links

Table of n, a(n) for n=1..58.

Example

a(7)=10 because the 7th composite is 14 and its remainders modulo 1, 2, 3, 4, 5, 6, 7 are 0, 0, 2, 2, 4, 2, 0 respectively and 0 + 0 + 2 + 2 + 4 + 2 + 0 = 10.

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: A162733 := proc(n) local c; c := A002808(n) ; add(c mod k, k=1..n) ; end: seq(A162733(n), n=1..80) ; # R. J. Mathar, Aug 01 2009

Mathematica

composite[n_] := FixedPoint[n + PrimePi[#] + 1 &, n + PrimePi[n] + 1];
a[n_] := Total[Mod[composite[n], #]& /@ Range[n]];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jul 23 2024 *)

Prog

(PARI) n=3; for(k=1, 100, n++; n+=isprime(n); print1(sum(i=1, k, n%i)", ")) \\ Franklin T. Adams-Watters, Aug 06 2009

Crossrefs

Cf. A002808, A099726.

Sequence in context: A058671 A016002 A098189 * A016003 A087139 A342607

Adjacent sequences: A162730 A162731 A162732 * A162734 A162735 A162736

Keyword

nonn,changed

Author

Juri-Stepan Gerasimov, Jul 13 2009

Extensions

Corrected and extended by R. J. Mathar and Franklin T. Adams-Watters, Aug 01 2009

Status

approved