A126073 -id:A126073 - cp's OEIS frontend

A126590 Multiples of 3 or 5 but not both.

3, 5, 6, 9, 10, 12, 18, 20, 21, 24, 25, 27, 33, 35, 36, 39, 40, 42, 48, 50, 51, 54, 55, 57, 63, 65, 66, 69, 70, 72, 78, 80, 81, 84, 85, 87, 93, 95, 96, 99, 100, 102, 108, 110, 111, 114, 115, 117, 123, 125, 126, 129, 130, 132, 138, 140, 141, 144, 145, 147, 153, 155, 156

Offset: 1

Zak Seidov, Mar 13 2007

Numbers n such that (n mod 3)*(n mod 5) = 0 and n mod 15 > 0.

			3, 5, 6, 9, 10, 12, (not 15), 18, 20, 21, 24, 25, 27, (not 30), 33, etc.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Cf. A126073, A126592.

I:=[3,5,6,9,10,12,18]; [n le 7 select I[n] else Self(n-1) + Self(n-6) - Self(n-7): n in [1..70]]; // G. C. Greubel, Mar 06 2018

s={}; Do[m3=Mod[n,3]; m5=Mod[n,5]; m15=Mod[n,15]; If[m3*m5==0&&m15>0,AppendTo[s,n]],{n,200}]; s

is(n)=isprime(gcd(n,15)) \\ Charles R Greathouse IV, Oct 11 2013

a(n) = a(n-1) + a(n-6) - a(n-7). - Charles R Greathouse IV, Oct 11 2013

A126592 Sum of numbers less than or equal to n which are multiples of 3 or 5.

Original entry on oeis.org

0, 0, 3, 3, 8, 14, 14, 14, 23, 33, 33, 45, 45, 45, 60, 60, 60, 78, 78, 98, 119, 119, 119, 143, 168, 168, 195, 195, 195, 225, 225, 225, 258, 258, 293, 329, 329, 329, 368, 408, 408, 450, 450, 450, 495, 495, 495, 543, 543, 593, 644, 644, 644, 698, 753, 753, 810, 810

Offset: 1

Zak Seidov, Mar 13 2007

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Project Euler, Problem 1: Multiples of 3 and 5
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).

Cf. A126073, A126590.

[(3*Floor(n/3)*(1 + Floor(n/3)) + 5*Floor(n/5)*(1 + Floor(n/5)) - 15*Floor(n/15)*(1 + Floor(n/15)))/2: n in [1..30]]; // G. C. Greubel, Mar 06 2018

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] - sn[n, 15], {n, 1000}]
Accumulate[Table[If[Divisible[n, 3] || Divisible[n, 5], n, 0], {n, 60}]] (* Harvey P. Dale, Jun 09 2016 *)
Accumulate[Table[n Boole[GCD[n, 15] > 1], {n, 50}]] (* Alonso del Arte, Dec 23 2018 *)

{b(n,x)=floor(n/x)*(1 + floor(n/x))};
for(n=1,30, print1((3*b(n,3) + 5*b(n,5) - 15*b(n,15))/2, ", ")) \\ G. C. Greubel, Mar 06 2018

(for (n <- 2 to 50) yield if ((n % 3) * (n % 5) == 0) { n } else { 0 }).scanLeft(0)( + ) // Alonso del Arte, Dec 23 2018

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) - sn(n, 15).

cp's OEIS Frontend

A126590 Multiples of 3 or 5 but not both.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula