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%I #18 Sep 01 2024 00:12:47
%S 1,2,4,8,3,6,12,24,9,18,36,72,27,54,108,216,5,10,20,40,15,30,60,120,
%T 45,90,180,360,135,270,540,1080,25,50,100,200,75,150,300,600,225,450,
%U 900,1800,675,1350,2700,5400,125,250,500,1000,375,750,1500,3000,1125
%N Write n in base 4 as n = b_0 + b_1*4 + b_2*4^2 + b_3*4^3 + ...; then a(n) = Product_{i >= 0} prime(i+1)^b_i.
%F a(4^k) = prime(k+1).
%e a(13) = a(1 + 3*4) = 2^1 * 3^3 = 54.
%e a(29) = a(1 + 3*4 + 1*4^2) = 2^1 * 3^3 * 5^1 = 270.
%p a:= n-> (l-> mul(ithprime(i)^l[i], i=1..nops(l)))(convert(n, base, 4)):
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Aug 31 2024
%t f[n_Integer, base_Integer] /; base >= 2 := Product[ Prime[i]^IntegerDigits[n, base][[Length[IntegerDigits[n, base]] + 1 - i]], {i, Length[IntegerDigits[n, base]]}] Table[f[i, 4], {i, 0, 45}]
%o (PARI)
%o f(n, b) = { my(d = digits(n,b), L = #d); prod(i=1, L, prime(i)^d[L+1-i]) }
%o apply(n -> f(n, 4), [0..45]) \\ _Satish Bysany_, Mar 07 2017
%Y Cf. A019565 (base 2), A101278 (base 3), A101943 (base 5), A054842 (base 10).
%K base,nonn,easy
%O 0,2
%A Orges Leka (oleka(AT)students.uni-mainz.de), Dec 21 2004