A126073 - OEIS

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

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OFFSET

1,3

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).

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].

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}]

CROSSREFS

Cf. A126590, A126592.

Sequence in context: A090597 A369084 A304887 * A126592 A055057 A154029

Adjacent sequences: A126070 A126071 A126072 * A126074 A126075 A126076

KEYWORD

nonn

AUTHOR

Zak Seidov, Mar 13 2007

STATUS

approved