A060904 -id:A060904 - cp's OEIS frontend

A243757 a(n) = Product_{i=1..n} A060904(i).

1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 25, 25, 25, 25, 25, 125, 125, 125, 125, 125, 625, 625, 625, 625, 625, 15625, 15625, 15625, 15625, 15625, 78125, 78125, 78125, 78125, 78125, 390625, 390625, 390625, 390625, 390625, 1953125, 1953125, 1953125, 1953125, 1953125, 9765625

Offset: 0

Tom Edgar, Jun 10 2014

nonn

This is the generalized factorial for A060904.
a(0) = 1 as it represents the empty product.
a(n) is the largest power of 5 that divides n!, or the order of a 5-Sylow subgroup of the symmetric group of degree n. - David Radcliffe, Sep 03 2021

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.

Cf. A027868, A060818, A060828, A060904, A242954.

a243757 n = a243757_list !! n
a243757_list = scanl (*) 1 a060904_list
-- Reinhard Zumkeller, Feb 04 2015

Table[Product[5^IntegerExponent[k, 5], {k, 1, n}], {n, 0, 20}] (* G. C. Greubel, Dec 24 2016 *)

a(n) = prod(k=1,n, 5^valuation(k,5)); \\ G. C. Greubel, Dec 24 2016

S=[0]+[5^valuation(i, 5) for i in [1..100]]
[prod(S[1:i+1]) for i in [0..99]]

a(n) = Product_{i=1..n} A060904(i).

a(n) = 5^(A027868(n)).

A264995 Bijective base-5 reverse: a(0) = 0; for n >= 1, a(n) = A030104(A132739(n)) * A060904(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 11, 16, 21, 10, 7, 12, 17, 22, 15, 8, 13, 18, 23, 20, 9, 14, 19, 24, 25, 26, 51, 76, 101, 30, 31, 56, 81, 106, 55, 36, 61, 86, 111, 80, 41, 66, 91, 116, 105, 46, 71, 96, 121, 50, 27, 52, 77, 102, 35, 32, 57, 82, 107, 60, 37, 62, 87, 112, 85, 42, 67, 92, 117, 110, 47, 72, 97, 122, 75, 28, 53, 78, 103, 40, 33

Offset: 0

Antti Karttunen, Dec 07 2015

Self-inverse permutation of nonnegative integers.

Antti Karttunen, Table of n, a(n) for n = 0..15625
Index entries for sequences that are permutations of the natural numbers

Cf. A010873, A030104, A060904, A132739.

Cf. similar sequences A057889 (base-2), A263273 (base-3), A264994 (base-4), A264979 (base-9).

(define (A264995 n) (if (zero? n) n (* (A030104 (A132739 n)) (A060904 n))))

a(0) = 0; for n >= 1, a(n) = A030104(A132739(n)) * A060904(n).
Other identities. For all n >= 0:
a(5*n) = 5*a(n).
A010873(a(n)) = 0 if and only if A010873(n) = 0 and it also seems that A010873(a(n)) = A010873(n) for all n.

A038500 Highest power of 3 dividing n.

Original entry on oeis.org

1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 81

Offset: 1

N. J. A. Sloane

To construct the sequence: start with 1 and concatenate twice: 1,1,1 then tripling the last term gives: 1,1,3. Concatenating those 3 terms twice gives: 1,1,3,1,1,3,1,1,3, triple the last term -> 1,1,3,1,1,3,1,1,9. Concatenating those 9 terms twice gives: 1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,9, triple the last term -> 1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,9,1,1,3,1,1,3,1,1,27 etc. - Benoit Cloitre, Dec 17 2002

Also 3-adic value of 1/n, n >= 1. See the Mahler reference, definition on p. 7. This is a non-archimedean valuation. See Mahler, p. 10. Sometimes also called 3-adic absolute value. - Wolfdieter Lang, Jun 28 2014

Kurt Mahler, p-adic numbers and their functions, second ed., Cambridge University Press, 1981.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
Zoran Sunic, Tree morphisms, transducers and integer sequences, arXiv:math/0612080 [math.CO], 2006.

Cf. A001620, A007949, A038502, A060904, A268354, A268357.

a038500 = f 1 where
   f y x = if m == 0 then f (y * 3) x' else y  where (x', m) = divMod x 3
-- Reinhard Zumkeller, Jul 06 2014

[3^Valuation(n,3): n in [1..100]]; // Vincenzo Librandi, Dec 29 2015

A038500 := n -> 3^padic[ordp](n,3): # Peter Luschny, Nov 26 2010

Flatten[{1,1,#}&/@(3^IntegerExponent[#,3]&/@(3*Range[40]))] (* or *) hp3[n_]:=If[Divisible[n,3],3^IntegerExponent[n,3],1]; Array[hp3,90] (* Harvey P. Dale, Mar 24 2012 *)
Table[3^IntegerExponent[n, 3], {n, 100}] (* Vincenzo Librandi, Dec 29 2015 *)

{a(n) = if( n<1, 0, 3^valuation(n, 3))};

Multiplicative with a(p^e) = p^e if p = 3, 1 otherwise. - Mitch Harris, Apr 19 2005
a(n) = n / A038502(n). Dirichlet g.f. zeta(s)*(3^s-1)/(3^s-3). - R. J. Mathar, Jul 12 2012
From Peter Bala, Feb 21 2019: (Start)
a(n) = gcd(n,3^n).
O.g.f.: x/(1 - x) + 2*Sum_{n >= 1} 3^(n-1)*x^(3^n)/ (1 - x^(3^n)). (End)
Sum_{k=1..n} a(k) ~ (2/(3*log(3)))*n*log(n) + (2/3 + 2*(gamma-1)/(3*log(3)))*n, where gamma is Euler's constant (A001620). - Amiram Eldar, Nov 15 2022

A132739 Largest divisor of n not divisible by 5.

Original entry on oeis.org

1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, 18, 19, 4, 21, 22, 23, 24, 1, 26, 27, 28, 29, 6, 31, 32, 33, 34, 7, 36, 37, 38, 39, 8, 41, 42, 43, 44, 9, 46, 47, 48, 49, 2, 51, 52, 53, 54, 11, 56, 57, 58, 59, 12, 61, 62, 63, 64, 13, 66, 67, 68, 69, 14, 71, 72, 73, 74, 3, 76, 77

Offset: 1

Reinhard Zumkeller, Aug 27 2007

A000265(a(n)) = a(A000265(n)) = A132740(n).
a(n) = A060791(n) when n is not divisible by 5. When n is divisible by 5 a(n) divides A060791(n). Tom Edgar, Feb 08 2014
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

			From _Peter Bala_, Feb 21 2019: (Start)
Sum_{n >= 1} n*a(n)*x^n = G(x) - (4*5)*G(x^5) - (4*25)*G(x^25) - (4*125)*G(x^125) - ..., where G(x) = x*(1 + x)/(1 - x)^3.
Sum_{n >= 1} (1/n)*a(n)*x^n = H(x) - (4/5)*H(x^5) - (4/25)*H(x^25) - (4/125)*H(x^125) - ..., where H(x) = x/(1 - x).
Sum_{n >= 1} (1/n^2)*a(n)*x^n = L(x) - (4/5^2)*L(x^5) - (4/25^2)*L(x^25) - (4/125^2)*L(x^125) - ..., where L(x) = Log(1/(1 - x)).
Also, Sum_{n >= 1} 1/a(n)*x^n = L(x) + (4/5)*L(x^5) + (4/5)*L(x^25) + (4/5)*L(x^125) + ....
(End)

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Peter Bala, A note on the sequence of numerators of a rational function, 2019.

Cf. A000265, A038502, A060791, A060904, A112765, A242603.

a132739 n | r > 0     = n
          | otherwise = a132739 n' where (n',r) = divMod n 5
-- Reinhard Zumkeller, Apr 08 2011

f[n_]:=Denominator[5^n/n];Array[f,100] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2011*)
Table[n/5^IntegerExponent[n, 5], {n, 100}] (* Amiram Eldar, Sep 15 2020 *)

a(n)=n/5^valuation(n, 5) /* Simon Strandgaard, Nov 01 2021 */

def A132739(n):
    a, b = divmod(n, 5)
    while b == 0:
        a, b = divmod(a,5)
    return 5*a+b # Chai Wah Wu, Dec 05 2021

p (1..50).map { |n| n /= 5 while (n % 5) == 0; n } # Simon Strandgaard, Nov 01 2021

a(n) = n/A060904(n). Dirichlet g.f.: zeta(s-1)*(5^s-5)/(5^s-1). - R. J. Mathar, Jul 12 2012
a(n) = n/5^A112765(n). See A060904. - Wolfdieter Lang, Jun 18 2014
From Peter Bala, Feb 21 2019: (Start)
a(n) = n/gcd(n,5^n).
O.g.f.: F(x) - 4*F(x^5) - 4*F(x^25) - 4*F(x^125) - ..., 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) - (5^m - 1)(F(m,x^5) + F(m,x^25) + F(m,x^125) + ...), 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)
Sum_{k=1..n} a(k) ~ (5/12) * n^2. - Amiram Eldar, Nov 28 2022

A355582 a(n) is the largest 5-smooth divisor of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 1, 12, 1, 2, 15, 16, 1, 18, 1, 20, 3, 2, 1, 24, 25, 2, 27, 4, 1, 30, 1, 32, 3, 2, 5, 36, 1, 2, 3, 40, 1, 6, 1, 4, 45, 2, 1, 48, 1, 50, 3, 4, 1, 54, 5, 8, 3, 2, 1, 60, 1, 2, 9, 64, 5, 6, 1, 4, 3, 10, 1, 72, 1, 2, 75, 4, 1, 6, 1, 80

Offset: 1

Amiram Eldar, Jul 08 2022

Amiram Eldar, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Graph - the asymptotic ratio (1000000 terms)

Cf. A006519, A007814, A007949, A038500, A051037, A060904, A065331, A112765, A132741, A165725, A355583, A355584.

Cf. A379005 (rgs-transform), A379006 (ordinal transform).

a[n_] := Times @@ ({2, 3, 5}^IntegerExponent[n, {2, 3, 5}]); Array[a, 100]

a(n) = 3^valuation(n, 3) * 5^valuation(n, 5) << valuation(n, 2);

from sympy import multiplicity as v
def a(n): return 2**v(2, n) * 3**v(3, n) * 5**v(5, n)
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Jul 08 2022

Multiplicative with a(p^e) = p^e if p <= 5 and 1 otherwise.
a(n) = A006519(n) * A038500(n) * A060904(n).
a(n) = 2^A007814(n) * 3^A007949(n) * 5^A112765(n).
a(n) = n / A165725(n).
Dirichlet g.f.: zeta(s)*(2^s-1)*(3^s-1)*(5^s-1)/((2^s-2)*(3^s-3)*(5^s-5)). - Amiram Eldar, Dec 25 2022
Sum_{k=1..n} a(k) ~ 2*n*log(n)^3 / (45*log(2)*log(3)*log(5)) + O(n*log(n)^2). - Vaclav Kotesovec, Apr 20 2025

A132741 Largest divisor of n having the form 2^i*5^j.

Original entry on oeis.org

1, 2, 1, 4, 5, 2, 1, 8, 1, 10, 1, 4, 1, 2, 5, 16, 1, 2, 1, 20, 1, 2, 1, 8, 25, 2, 1, 4, 1, 10, 1, 32, 1, 2, 5, 4, 1, 2, 1, 40, 1, 2, 1, 4, 5, 2, 1, 16, 1, 50, 1, 4, 1, 2, 5, 8, 1, 2, 1, 20, 1, 2, 1, 64, 5, 2, 1, 4, 1, 10, 1, 8, 1, 2, 25, 4, 1, 2, 1, 80, 1, 2, 1, 4, 5, 2, 1, 8, 1, 10, 1, 4, 1, 2, 5, 32, 1, 2

Offset: 1

Reinhard Zumkeller, Aug 27 2007

The range of this sequence, { a(n); n>=0 }, is equal to A003592. - M. F. Hasler, Dec 28 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A003592, A006519, A007732, A007814, A051626, A060904, A112765, A132740.
Cf. A001620, A082633.
Cf. A379003 (ordinal transform), A379004 (rgs-transform).
Cf. also A355582.

a132741 = f 2 1 where
   f p y x | r == 0    = f p (y * p) x'
           | otherwise = if p == 2 then f 5 y x else y
           where (x', r) = divMod x p
-- Reinhard Zumkeller, Nov 19 2015

A132741 := proc(n) local f,a; f := ifactors(n)[2] ; a := 1; for f in ifactors(n)[2] do if op(1,f) =2 then a := a*2^op(2,f) ; elif op(1,f) =5 then a := a*5^op(2,f) ; end if; end do;a; end proc: # R. J. Mathar, Sep 06 2011

a[n_] := SelectFirst[Reverse[Divisors[n]], MatchQ[FactorInteger[#], {{1, 1}} | {{2, }} | {{5, }} | {{2, }, {5, }}]&]; Array[a, 100] (* Jean-François Alcover, Feb 02 2018 *)
a[n_] := Times @@ ({2, 5}^IntegerExponent[n, {2, 5}]); Array[a, 100] (* Amiram Eldar, Jun 12 2022 *)

A132741(n)=5^valuation(n,5)<M. F. Hasler, Dec 28 2015

a(n) = n / A132740(n).
a(A003592(n)) = A003592(n).
A051626(a(n)) = 0.
A007732(a(n)) = 1.
From R. J. Mathar, Sep 06 2011: (Start)
Multiplicative with a(2^e)=2^e, a(5^e)=5^e and a(p^e)=1 for p=3 or p>=7.
Dirichlet g.f. zeta(s)*(2^s-1)*(5^s-1)/((2^s-2)*(5^s-5)). (End)
a(n) = A006519(n)*A060904(n) = 2^A007814(n)*5^A112765(n). - M. F. Hasler, Dec 28 2015
Sum_{k=1..n} a(k) ~ n*(12*log(n)^2 + (24*gamma + 36*log(2) - 24)*log(n) + 24 - 24*gamma - 36*log(2) + 36*gamma*log(2) + 2*log(2)^2 - 18*log(5) + 18*gamma*log(5) + 27*log(2)*log(5) + 2*log(5)^2 + 18*log(5)*log(n) - 24*gamma_1)/(60*log(2)*log(5)), where gamma is Euler's constant (A001620) and gamma_1 is the first Stieltjes constant (A082633). - Amiram Eldar, Jan 26 2023

A093348 A 5-fractal "castle" starting with 0.

Original entry on oeis.org

0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24, 25, 24, 25, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24

Offset: 1

Benoit Cloitre, Apr 26 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Benoit Cloitre, Graph of a(n) for n=1 up to 25
Benoit Cloitre, Graph of a(n) for n=1 up to 125
Benoit Cloitre, Graph of a(n) for n=1 up to 625

Cf. A093347, A093349.

Cf. A060904.

a[n_] := Sum[(-1)^(i+1) * 5^IntegerExponent[i, 5], {i, 1, n-1}]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)

a(n)=if(n<2,0,5^floor(log(n-1)/log(5))-a(n-5^floor(log(n-1)/log(5))))

a(1) = 0, then a(n) = w(n) - a(n-w(n)) where w(n) = 5^floor(log(n-1)/log(5)).
a(n) = Sum_{i=1..n-1} (-1)^(i-1)*5^valuation(i, 5).
Conjecture: a(n+1) = (n mod 2) + Sum_{k=0..infinity} (4*5^k*(floor(n/5^(k+1)) mod 2)). - Charlie Neder, May 25 2019

A268354 Highest power of 7 dividing n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 7

Offset: 1

Tom Edgar, Feb 02 2016

The generalized binomial coefficients produced by this sequence provide an analog to Kummer's Theorem using arithmetic in base 7.

			Since 14 = 7 * 2, a(14) = 7. Likewise, since 7 does not divide 13, a(13) = 1.

Antti Karttunen, Table of n, a(n) for n = 1..20790
Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

Cf. A000420, A001620, A006519, A038500, A234957, A214411, A234959, A060904, A242603, A268357.

[7^Valuation(n,7): n in [1..150]]; // Vincenzo Librandi, Feb 03 2016

7^Table[IntegerExponent[n, 7], {n, 150}] (* Vincenzo Librandi, Feb 03 2016 *)

a(n) = 7^valuation(n, 7) \\ Michel Marcus, Feb 05 2016

Sage
```
[7^valuation(i, 7) for i in [1..100]]
```

a(n) = 7^valuation(n,7).
a(n) = 7^A214411(n).
Completely multiplicative with a(7) = 7, a(p) = 1 for prime p and p <> 7. - Andrew Howroyd, Jul 20 2018
From Peter Bala, Feb 21 2019: (Start)
a(n) = gcd(n,7^n).
a(n) = n/A242603(n).
O.g.f.: x/(1 - x) + 6*Sum_{n >= 1} 7^(n-1)*x^(7^n)/ (1 - x^(7^n)). (End)
Sum_{k=1..n} a(k) ~ (6/(7*log(7)))*n*log(n) + (4/7 + 6*(gamma-1)/(7*log(7)))*n, where gamma is Euler's constant (A001620). - Amiram Eldar, Nov 15 2022
Dirichlet g.f.: zeta(s)*(7^s-1)/(7^s-7). - Amiram Eldar, Jan 03 2023

More terms from Antti Karttunen, Dec 22 2017

A268357 Highest power of 11 dividing n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 121, 1

Offset: 1

Tom Edgar, Feb 02 2016

The generalized binomial coefficients produced by this sequence provide an analog to Kummer's Theorem using arithmetic in base 11.

This first index where this differs from A109014 is 121; a(121) = 121 and A109014(121) = 11.

			Since 22 = 11 * 2, a(22) = 11. Likewise, since 11 does not divide 21, a(21) = 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

Cf. A001620, A006519, A038500, A234957, A234959, A109014, A268354, A060904.

[11^Valuation(n,11): n in [1..130]]; // Vincenzo Librandi, Feb 03 2016

Table[11^IntegerExponent[n, 11], {n, 130}] (* Bruno Berselli, Feb 03 2016 *)

[11^valuation(i, 11) for i in [1..130]]

a(n) = 11^valuation(n,11).
Completely multiplicative with a(11) = 11, a(p) = 1 for prime p and p<>11. - Andrew Howroyd, Jul 20 2018
From Peter Bala, Feb 21 2019: (Start)
a(n) = gcd(n,11^n).
O.g.f.: x/(1 - x) + 10*Sum_{n >= 1} 11^(n-1)*x^(11^n)/ (1 - x^(11^n)). (End)
Sum_{k=1..n} a(k) ~ (10/(11*log(11)))*n*log(n) + (6/11 + 10*(gamma-1)/(11*log(11)))*n, where gamma is Euler's constant (A001620). - Amiram Eldar, Nov 15 2022
Dirichlet g.f.: zeta(s)*(11^s-1)/(11^s-11). - Amiram Eldar, Jan 03 2023

A060865 a(n) is the exact power of 2 that divides the n-th Fibonacci number (A000045).

Original entry on oeis.org

1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 64, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 16, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 128, 1, 1, 2, 1

Offset: 1

Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001

			a(12) = 16 because the 12th Fibonacci number is 144 and 144 = 9*16.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000045, A060904(n) = 5^A112765(n), A090740.

seq(2^padic:-ordp(combinat:-fibonacci(n),2),n=1..100); # Robert Israel, Dec 28 2015

Table[2^IntegerExponent[Fibonacci[n],2],{n,100}] (* Harvey P. Dale, Aug 04 2025 *)

a(n)=2^valuation(fibonacci(n), 2) \\Michel Marcus, Jul 30 2013

If n is not divisible by 3 then a(n) = 1, if n = 3 * 2^k * (2m + 1) then a(n) = 2 if k=0 or 2^(k+2) if k>0.
a(n) = F(n) / A174883(n). - Franklin T. Adams-Watters, Jan 24 2012
a(n) = A006519(A000045(n)). - Michel Marcus, Jul 30 2013
a(3n) = 2^A090740(n). - Robert Israel, Dec 28 2015

More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001

cp's OEIS Frontend

A243757 a(n) = Product_{i=1..n} A060904(i).

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A264995 Bijective base-5 reverse: a(0) = 0; for n >= 1, a(n) = A030104(A132739(n)) * A060904(n).

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A038500 Highest power of 3 dividing n.

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A132739 Largest divisor of n not divisible by 5.

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A355582 a(n) is the largest 5-smooth divisor of n.

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A132741 Largest divisor of n having the form 2^i*5^j.

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A093348 A 5-fractal "castle" starting with 0.

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