A178144 Sum of divisors d of n which are d=2, 3 or 5.

0, 2, 3, 2, 5, 5, 0, 2, 3, 7, 0, 5, 0, 2, 8, 2, 0, 5, 0, 7, 3, 2, 0, 5, 5, 2, 3, 2, 0, 10, 0, 2, 3, 2, 5, 5, 0, 2, 3, 7, 0, 5, 0, 2, 8, 2, 0, 5, 0, 7, 3, 2, 0, 5, 5, 2, 3, 2, 0, 10, 0, 2, 3, 2, 5, 5, 0, 2, 3, 7, 0, 5, 0, 2, 8, 2, 0, 5, 0, 7, 3, 2, 0, 5, 5, 2, 3, 2, 0, 10, 0, 2, 3, 2, 5, 5, 0, 2, 3, 7, 0, 5, 0, 2, 8

Offset

1,2

Comments

The sequence is periodic with period length 30.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Vladimir Shevelev, A recursion for divisor function over divisors belonging to a prescribed finite sequence of positive integers and a solution of the Lahiri problem for divisor function sigma_x(n), arXiv:0903.1743 [math.NT], 2009.

Index entries for linear recurrences with constant coefficients, signature (-2,-2,-1,0,1,2,2,1).

Formula

From R. J. Mathar, Jul 23 2012: (Start)

a(n) = -2*a(n-1) -2*a(n-2) -a(n-3) +a(n-5) +2*a(n-6) +2*a(n-7) +a(n-8).

G.f.: ( -x*(2+7*x+12*x^2+17*x^3+22*x^4+10*x^6+20*x^5) ) / ( (x-1)*(1+x)*(1+x+x^2)*(x^4+x^3+x^2+x+1) ). (End)

Maple

A178144 := proc(n)
    local a;
    a := 0 ;
    for d in {2, 3, 5} do
        if (n mod d) = 0 then
            a := a+d ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Jul 23 2012

Mathematica

a[n_] := DivisorSum[n, Boole[MatchQ[#, 2|3|5]]*#&];
Array[a, 105] (* Jean-François Alcover, Nov 24 2017 *)
a[n_] := Sum[d * Boole[Divisible[n, d]], {d, {2, 3, 5}}]; Array[a, 100] (* Amiram Eldar, Dec 20 2024 *)

Prog

(PARI) a(n) = sumdiv(n, d, if ((d==2) || (d==3) || (d==5), d)); \\ Michel Marcus, Nov 24 2017
(PARI) a(n) = my(d = [2, 3, 5]); sum(k = 1, 3, d[k] * !(n % d[k])); \\ Amiram Eldar, Dec 20 2024

Crossrefs

Cf. A000203, A008472, A178143, A171182, A178142.

Sequence in context: A268466 A075274 A331309 * A357987 A135737 A125179

Adjacent sequences: A178141 A178142 A178143 * A178145 A178146 A178147

Keyword

nonn,easy

Author

Vladimir Shevelev, May 21 2010

Status

approved