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A178142 Sum over the divisors d = 2 and/or 3 of n. 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, 2, 0, 5, 0, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..105.

V. 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).

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) = (1/30)*{29*[(n-1) mod 6]-21*(n mod 6)+14*[(n+1) mod 6]+9*[(n+2) mod 6]-[(n+3) mod 6]-6*[(n+4) mod 6]}, with n>=1. [Paolo P. Lava, May 24 2010]

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 *)

PROG

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

CROSSREFS

Cf. A000203, A008472, A178143.

Sequence in context: A056888 A286297 A111182 * A076427 A284152 A011024

Adjacent sequences:  A178139 A178140 A178141 * A178143 A178144 A178145

KEYWORD

nonn,easy,less

AUTHOR

Vladimir Shevelev, May 21 2010

EXTENSIONS

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

STATUS

approved

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Last modified October 18 05:18 EDT 2019. Contains 328146 sequences. (Running on oeis4.)