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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

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 December 5 09:53 EST 2022. Contains 358585 sequences. (Running on oeis4.)