A130779 - OEIS

A130779

a(0)=a(1)=1, a(2)=2, a(n)=0 for n >= 3.

1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

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OFFSET

0,3

COMMENTS

Inverse binomial transform of A002522. - R. J. Mathar, Jun 13 2008

Multiplicative with a(2)=2, a(2^e)=0 if e>1, a(p^e)=0 for odd prime p if e>=1. Dirichlet g.f. 1+2^(1-s). - R. J. Mathar, Jun 28 2011

a(n-1) is the determinant of the symmetric n X n matrix M(i,j) = rad(gcd(i,j)) for 1 <= i, j <= n, where rad(n) is the largest squarefree number dividing n (A007947). - Amiram Eldar, Jul 19 2019

REFERENCES

J. Sándor and B. Crstici, Handbook of Number Theory II, Kluwer, 2004, p. 265.

LINKS

Table of n, a(n) for n=0..104.

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

G.f.: 1+x+2x^2.

a(n) = A167666(n,0). - Philippe Deléham, Feb 18 2012

a(n) = n! mod 3. - Charles Kusniec, Jan 25 2020

MATHEMATICA

PadRight[{1, 1, 2}, 120, 0] (* Harvey P. Dale, May 02 2015 *)

LinearRecurrence[{1}, {1, 1, 2, 0}, 105] (* Ray Chandler, Jul 15 2015 *)