A178142 Sum over the divisors d = 2 and/or 3 of n.

0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3, 2, 0, 5, 0, 2, 3

Offset: 1

Author

Vladimir Shevelev, May 21 2010

Keywords

• nonn
• easy
• less

Comments

Periodic with period {0,2,3,2,0,5}.

Links

• 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 (-1,0,1,1).

Crossrefs

Cf. A000203, A008472, A010673, A021337, A171405, A178143.

Programs

Mathematica

Table[Total@ Select[Divisors@ n, 2 <= # <= 3 &], {n, 120}] (* or *)
Table[Total[Divisors@ n /. {d_ /; d < 2 -> Nothing, d_ /; d > 3 -> Nothing} ], {n, 120}] (* Michael De Vlieger, Feb 07 2016 *)
Flatten[Table[{0,2,3,2,0,5}, {16}]] (* Amiram Eldar, Aug 03 2024 *)

PARI

a(n) = sumdiv(n, d, d*((d==2) || (d==3))); \\ Michel Marcus, Feb 07 2016

PARI

a(n) = [0,2,3,2,0,5][(n-1) % 6 + 1]; \\ Amiram Eldar, Aug 03 2024

Formula

a(n) = Sum_{d|n, d=2 or d=3} d.

a(n+6) = a(n).

a(n) = -a(n-1) + a(n-3) + a(n-4).

G.f.: -x*(2+5*x+5*x^2) / ( (x-1)*(1+x)*(1+x+x^2) ).

a(n) = A010673(n) + A021337(n). - R. J. Mathar, May 28 2010

a(n) = A000203(n) - A171405(n). - Amiram Eldar, Aug 03 2024

Extensions

Replaced recurrence by a shorter one; added keyword:less - R. J. Mathar, May 28 2010