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A178146 a(n) is the number of distinct divisors d of n of the form d=2,3 or 5 1
0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 1, 1, 0, 3, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 1, 1, 0, 3, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 1, 1, 0, 3, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

The sequence is periodic with period {0 1 1 1 1 2 0 1 1 2 0 2 0 1 2 1 0 2 0 2 1 1 0 2 1 1 1 1 0 3} of length 30. There are 26 coincidences on the interval [1,30] with A156542.

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 (-2,-2,-1,0,1,2,2,1).

FORMULA

a(2)=1, a(3)=1, a(7)=0, a(8)=1, a(10)=2, otherwise, a(n)=a(n-2)+a(n-3)-a(n-7)-a(n-8)+a(n-10), where we put a(n)=0, if n<0.

G.f.: -x^2*(3*x^6+6*x^5+7*x^4+6*x^3+5*x^2+3*x+1) / ((x-1)*(x+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Mar 13 2013

MATHEMATICA

CoefficientList[Series[-x^2*(3*x^6 + 6*x^5 + 7*x^4 + 6*x^3 + 5*x^2 + 3*x + 1)/((x - 1)*(x + 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* G. C. Greubel, May 16 2017 *)

PROG

(PARI) x='x+O('x^50); concat([0], Vec(-x^2*(3*x^6+6*x^5+7*x^4+6*x^3+5*x^2+3*x+1)/((x-1)*(x+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)))) \\ G. C. Greubel, May 16 2017

CROSSREFS

Cf. A000005 A001221 A178144 A156542 A178143 A171182 A178142

Sequence in context: A130027 A116949 A204427 * A305435 A114708 A084927

Adjacent sequences:  A178143 A178144 A178145 * A178147 A178148 A178149

KEYWORD

nonn,uned,easy

AUTHOR

Vladimir Shevelev, May 21 2010

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)