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