A126073 Sum of numbers <= n which are multiples of 3 or 5 but not 15.

0, 0, 3, 3, 8, 14, 14, 14, 23, 33, 33, 45, 45, 45, 45, 45, 45, 63, 63, 83, 104, 104, 104, 128, 153, 153, 180, 180, 180, 180, 180, 180, 213, 213, 248, 284, 284, 284, 323, 363, 363, 405, 405, 405, 405, 405, 405, 453, 453, 503, 554, 554, 554, 608, 663, 663, 720, 720

Offset: 1

Author

Zak Seidov, Mar 13 2007

Keywords

• nonn

Comments

Sum of numbers m<=n such that mod(m,3)*mod(m,5)=0 and mod(m,15)>0.

First differences (fd) are

0,3,0,5,6,0,0,9,10,0,12,0,0,0,0,

0,18,0,20,21,0,0,24,25,0,27,0,0,0,0,

0,33,0,35,36,0,0,39,40,0,42,0,0,0,0,...

fd(1..15)={0,3,0,5,6,0,0,9,10,0,12,0,0,0,0}; for n>15

fd(n)=fd(n-15)+15 if fd(n-15)>0, fd(n)=0 otherwise.

Links

• Ray Chandler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Crossrefs

Cf. A126590, A126592.

Programs

Mathematica

an[n_,d_]:=d*Floor[n/d];sn[n_,d_]:=(an[n,d]*(an[n,d] + d))/(2*d); Table[sn[n,3]+sn[n,5]-2*sn[n,15],{n,1000}]
Accumulate[Table[If[Mod[n,3]Mod[n,5]==0&&Mod[n,15]>0,n,0],{n,60}]] (* Harvey P. Dale, Jul 19 2025 *)

Formula

an[n,d]=d*Floor[n/d];sn[n,d]=(an[n,d]*(an[n,d] + d))/(2*d); a(n)=sn[n,3]+sn[n,5]-2*sn[n,15].