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A178142
Sum over the divisors d = 2 and/or 3 of n.
6
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
1,2
COMMENTS
Periodic with period {0,2,3,2,0,5}.
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
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 *)
PROG
(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
CROSSREFS
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