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 A065883 Remove factors of 4 from n (i.e., write n in base 4, drop final zeros, then rewrite in decimal). 15
 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, 7, 29, 30, 31, 2, 33, 34, 35, 9, 37, 38, 39, 10, 41, 42, 43, 11, 45, 46, 47, 3, 49, 50, 51, 13, 53, 54, 55, 14, 57, 58, 59, 15, 61, 62, 63, 1, 65, 66, 67, 17, 69, 70, 71, 18, 73, 74, 75 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Indranil Ghosh, Table of n, a(n) for n = 1..20000 (First 1000 terms from Harry J. Smith) FORMULA If n mod 4 = 0 then a(n) = a(n/4), otherwise a(n) = n. Multiplicative with a(p^e) = 2^(e (mod 2)) if p = 2 and a(p^e) = p^e if p is an odd prime. a(n) = n/4^A235127(n). a(n) = A214392(n) if n mod 16 != 0. - Peter Kagey, Sep 02 2015 From Robert Israel, Dec 08 2015: (Start) G.f.: x/(1-x)^2 - 3 Sum_{j>=1} x^(4^j)/(1-x^(4^j))^2. G.f. satisfies G(x) = G(x^4) + x/(1-x)^2 - 4 x^4/(1-x^4)^2. (End) Sum_{k=1..n} a(k) ~ (2/5) * n^2. - Amiram Eldar, Nov 20 2022 Dirichlet g.f.: zeta(s-1)*(4^s-4)/(4^s-1). - Amiram Eldar, Jan 04 2023 EXAMPLE 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. MAPLE A065883:= n -> n/4^floor(padic:-ordp(n, 2)/2): map(A065883, [\$1..1000]); # Robert Israel, Dec 08 2015 MATHEMATICA If[Divisible[#, 4], #/4^IntegerExponent[#, 4], #]&/@Range[80] (* Harvey P. Dale, Aug 31 2013 *) PROG (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) } { 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 (PARI) a(n)=n/4^valuation(n, 4); \\ Joerg Arndt, Dec 09 2015 (Python) def A065883(n): return n>>((~n&n-1).bit_length()&-2) # Chai Wah Wu, Jul 09 2022 CROSSREFS Cf. A214392, A235127, A350091 (drop final 2's). Remove other factors: A000265, A038502, A132739, A244414, A242603, A004151. Sequence in context: A083346 A319652 A327938 * A214392 A071975 A350389 Adjacent sequences: A065880 A065881 A065882 * A065884 A065885 A065886 KEYWORD base,easy,nonn,mult AUTHOR Henry Bottomley, Nov 26 2001 STATUS approved

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Last modified April 20 06:37 EDT 2024. Contains 371799 sequences. (Running on oeis4.)