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

%I A126073 #7 Jul 19 2025 10:40:24
%S A126073 0,0,3,3,8,14,14,14,23,33,33,45,45,45,45,45,45,63,63,83,104,104,104,
%T A126073 128,153,153,180,180,180,180,180,180,213,213,248,284,284,284,323,363,
%U A126073 363,405,405,405,405,405,405,453,453,503,554,554,554,608,663,663,720,720
%N A126073 Sum of numbers <= n which are multiples of 3 or 5 but not 15.
%C A126073 Sum of numbers m<=n such that mod(m,3)*mod(m,5)=0 and mod(m,15)>0.
%C A126073 First differences (fd) are
%C A126073 0,3,0,5,6,0,0,9,10,0,12,0,0,0,0,
%C A126073 0,18,0,20,21,0,0,24,25,0,27,0,0,0,0,
%C A126073 0,33,0,35,36,0,0,39,40,0,42,0,0,0,0,...
%C A126073 fd(1..15)={0,3,0,5,6,0,0,9,10,0,12,0,0,0,0}; for n>15
%C A126073 fd(n)=fd(n-15)+15 if fd(n-15)>0, fd(n)=0 otherwise.
%H A126073 Ray Chandler, <a href="/A126073/b126073.txt">Table of n, a(n) for n = 1..1000</a>
%H A126073 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A126073 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].
%t A126073 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}]
%t A126073 Accumulate[Table[If[Mod[n,3]Mod[n,5]==0&&Mod[n,15]>0,n,0],{n,60}]] (* _Harvey P. Dale_, Jul 19 2025 *)
%Y A126073 Cf. A126590, A126592.
%K A126073 nonn
%O A126073 1,3
%A A126073 _Zak Seidov_, Mar 13 2007