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%I #20 Jul 19 2022 07:28:24
%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.
%C A permutation of the cubefree numbers (A004709). - _Rémy Sigrist_, Jul 18 2022
%H Reinhard 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
%Y Cf. A004709.
%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
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