This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A038502 Remove 3's from n. 36
 1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 13, 14, 5, 16, 17, 2, 19, 20, 7, 22, 23, 8, 25, 26, 1, 28, 29, 10, 31, 32, 11, 34, 35, 4, 37, 38, 13, 40, 41, 14, 43, 44, 5, 46, 47, 16, 49, 50, 17, 52, 53, 2, 55, 56, 19, 58, 59, 20, 61, 62, 7, 64, 65, 22, 67, 68, 23, 70, 71, 8, 73, 74, 25, 76 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As well as being multiplicative, a(n) is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for n, m >= 1. In particular, a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, Feb 21 2019 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(p^e) = 1 if p = 3, else p^e. - Mitch Harris, Apr 19 2005 a(0) = 0, a(3n) = a(n), a(3n+1) = 3n+1, a(3n+2) = 3n+2. Dirichlet g.f. zeta(s-1)*(3^s-3)/(3^s-1). - R. J. Mathar, Feb 11 2011 From Peter Bala, Feb 21 2019: (Start) a(n) = n/gcd(n,3^n). O.g.f.: F(x) - 2*F(x^3) - 2*F(x^9) - 2*F(x^27) - ..., where F(x) = x/(1 - x)^2 is the generating function for the positive integers. More generally, for m >= 1, Sum_{n >= 0} a(n)^m*x^n = F(m,x) - (3^m - 1)( F(m,x^3) + F(m,x^9) + F(m,x^27) + ... ), where F(m,x) = A(m,x)/(1 - x)^(m+1) with A(m,x) the m_th Eulerian polynomial: A(1,x) = x, A(2,x) = x*(1 + x), A(3,x) = x*(1 + 4*x + x^2) - see A008292. Repeatedly applying the Euler operator x*d/dx or its inverse operator to the o.g.f. for the sequence produces generating functions for the sequences n^m*a(n), m in Z. Some examples are given below. (End) EXAMPLE From Peter Bala, Feb 21 2019: (Start) Sum_{n >= 1} n*a(n)*x^n = G(x) - (2*3)*G(x^3) - (2*9)*G(x^9) - (2*27)*G(x^27) - ..., where G(x) = x*(1 + x)/(1 - x)^3. Sum_{n >= 1} (1/n)*a(n)*x^n = H(x) - (2/3)*H(x^3) - (2/9)*H(x^9) - (2/27)*H(x^27) - ..., where H(x) = x/(1 - x). Sum_{n >= 1} (1/n^2)*a(n)*x^n = L(x) - (2/3^2)*L(x^3) - (2/9^2)*L(x^9) - (2/27^2)*L(x^27) - ..., where L(x) = Log(1/(1 - x)). Also, Sum_{n >= 1} 1/a(n)*x^n = L(x) + (2/3)*L(x^3) + (2/3)*L(x^9) + (2/3)*L(x^27) + .... (End) MATHEMATICA f[n_] := Times @@ (First@#^Last@# & /@ Select[ FactorInteger@n, First@# != 3 &]); Array[f, 76] (* Robert G. Wilson v, Jul 31 2006 *) f[n_]:=Denominator[3^n/n]; Array[f, 100] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2011 *) PROG (PARI) a(n)=if(n<1, 0, n/3^valuation(n, 3)) /* Michael Somos, Nov 10 2005 */ (Haskell) a038502 n = if m > 0 then n else a038502 n'  where (n', m) = divMod n 3 -- Reinhard Zumkeller, Jan 03 2011 (MAGMA) [n/3^Valuation(n, 3): n in [1..80]]; // Bruno Berselli, May 21 2013 CROSSREFS Cf. A007949, A038500, A000265 (remove 2's), A065330, A065883 (remove 4's), A132739 (remove 5's), A242603 (remove 7's). Sequence in context: A065518 A072012 A172500 * A106610 A182398 A214736 Adjacent sequences:  A038499 A038500 A038501 * A038503 A038504 A038505 KEYWORD nonn,easy,mult AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 23 09:24 EDT 2019. Contains 328345 sequences. (Running on oeis4.)