# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a065883 Showing 1-1 of 1 %I A065883 #65 Jan 04 2023 02:10:01 %S A065883 1,2,3,1,5,6,7,2,9,10,11,3,13,14,15,1,17,18,19,5,21,22,23,6,25,26,27, %T A065883 7,29,30,31,2,33,34,35,9,37,38,39,10,41,42,43,11,45,46,47,3,49,50,51, %U A065883 13,53,54,55,14,57,58,59,15,61,62,63,1,65,66,67,17,69,70,71,18,73,74,75 %N A065883 Remove factors of 4 from n (i.e., write n in base 4, drop final zeros, then rewrite in decimal). %H A065883 Indranil Ghosh, Table of n, a(n) for n = 1..20000 (First 1000 terms from Harry J. Smith) %F A065883 If n mod 4 = 0 then a(n) = a(n/4), otherwise a(n) = n. %F A065883 Multiplicative with a(p^e) = 2^(e (mod 2)) if p = 2 and a(p^e) = p^e if p is an odd prime. %F A065883 a(n) = n/4^A235127(n). %F A065883 a(n) = A214392(n) if n mod 16 != 0. - _Peter Kagey_, Sep 02 2015 %F A065883 From _Robert Israel_, Dec 08 2015: (Start) %F A065883 G.f.: x/(1-x)^2 - 3 Sum_{j>=1} x^(4^j)/(1-x^(4^j))^2. %F A065883 G.f. satisfies G(x) = G(x^4) + x/(1-x)^2 - 4 x^4/(1-x^4)^2. (End) %F A065883 Sum_{k=1..n} a(k) ~ (2/5) * n^2. - _Amiram Eldar_, Nov 20 2022 %F A065883 Dirichlet g.f.: zeta(s-1)*(4^s-4)/(4^s-1). - _Amiram Eldar_, Jan 04 2023 %e A065883 a(7)=7, a(14)=14, a(28)=a(4*7)=7, a(56)=a(4*14)=14, a(112)=a(4^2*7)=7. %p A065883 A065883:= n -> n/4^floor(padic:-ordp(n,2)/2): %p A065883 map(A065883, [$1..1000]); # _Robert Israel_, Dec 08 2015 %t A065883 If[Divisible[#,4],#/4^IntegerExponent[#,4],#]&/@Range[80] (* _Harvey P. Dale_, Aug 31 2013 *) %o A065883 (PARI) baseA2B(x, a, b)= { local(d, e=0, f=1); while (x>0, d=x%b; x\=b; e+=d*f; f*=a); return(e) } %o A065883 { for (n=1, 1000, if (n%4, a=n, a=baseA2B(n, 10, 4); while (a%10 == 0, a\=10); a=baseA2B(a, 4, 10)); write("b065883.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 03 2009 %o A065883 (PARI) a(n)=n/4^valuation(n,4); \\ _Joerg Arndt_, Dec 09 2015 %o A065883 (Python) %o A065883 def A065883(n): return n>>((~n&n-1).bit_length()&-2) # _Chai Wah Wu_, Jul 09 2022 %Y A065883 Cf. A214392, A235127, A350091 (drop final 2's). %Y A065883 Remove other factors: A000265, A038502, A132739, A244414, A242603, A004151. %K A065883 base,easy,nonn,mult %O A065883 1,2 %A A065883 _Henry Bottomley_, Nov 26 2001 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE