login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101278 Write n in base 3 as n = b_0 + b_1*3 + b_2*3^2 + b_3*3^3 + ...; then a(n) = Product_{i >= 0} prime(i+1)^b_i. 5

%I

%S 1,2,4,3,6,12,9,18,36,5,10,20,15,30,60,45,90,180,25,50,100,75,150,300,

%T 225,450,900,7,14,28,21,42,84,63,126,252,35,70,140,105,210,420,315,

%U 630,1260,175,350,700,525,1050,2100,1575,3150,6300,49,98,196,147,294,588

%N Write n in base 3 as n = b_0 + b_1*3 + b_2*3^2 + b_3*3^3 + ...; then a(n) = Product_{i >= 0} prime(i+1)^b_i.

%C One may generate other sequences by changing the base b.

%H R. Zumkeller, <a href="/A101278/b101278.txt">Table of n, a(n) for n = 0..6560</a>

%F If a(bn)=x then a(bn+1)=2x, a(bn+2)=4x, ... a(bn+b-1)=2^b*x. - _Robert G. Wilson v_, Dec 24 2004

%F G.f.: (1+2x+4x^2)(1+3x^3+9x^6)(1+5x^9+25x^18)... - _Paul Boddington_, Jul 21 2005

%F a(n) = f(n, 1, 1) with f(x, y, z) = if x > 0 then f(floor(x/3), y*prime(z)^(x mod 3), z+1) else y. - _Reinhard Zumkeller_, Mar 13 2010

%e The first few terms are computed as follows:

%e n b2 b1 b0 a(n)

%e 0, 0, 0, 0, 1

%e 1, 0, 0, 1, 2

%e 2, 0, 0, 2, 4

%e 3, 0, 1, 0, 3

%e 4, 0, 1, 1, 6

%e 5, 0, 1, 2, 12

%t primeBase[n_Integer?Positive, base_Integer]/;base>1 := Times @@ (Table[Prime[i], {i, Floor[Log[base, n] + 1], 1, -1}]^IntegerDigits[n, base]); Table[primeBase[n, 3], {n, 59}] (* _Robert G. Wilson v_, Dec 24 2004 *)

%Y Cf. A019565, A054842. - _Reinhard Zumkeller_, Mar 13 2010

%K nonn,easy

%O 0,2

%A Orges Leka (oleka(AT)students.uni-mainz.de), Dec 20 2004

%E More terms from _Robert G. Wilson v_, Dec 24 2004

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 16:36 EST 2019. Contains 329323 sequences. (Running on oeis4.)