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Write n in base 5 as n = b_0 + b_1*5 + b_2*5^2 + b_3*5^3 + ...; then a(n) = Product_{i >= 0} prime(i+1)^b_i.
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%I #14 Sep 01 2024 00:13:00

%S 1,2,4,8,16,3,6,12,24,48,9,18,36,72,144,27,54,108,216,432,81,162,324,

%T 648,1296,5,10,20,40,80,15,30,60,120,240,45,90,180,360,720,135,270,

%U 540,1080,2160,405,810,1620,3240,6480,25,50,100,200,400,75,150,300,600

%N Write n in base 5 as n = b_0 + b_1*5 + b_2*5^2 + b_3*5^3 + ...; then a(n) = Product_{i >= 0} prime(i+1)^b_i.

%e a(29) = a(4 + 0*5 + 1*5^2) = 2^4 * 3^0 * 5^1 = 80.

%p a:= n-> (l-> mul(ithprime(i)^l[i], i=1..nops(l)))(convert(n, base, 5)):

%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, 5], {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, 5), [0..45]) \\ _Satish Bysany_, Mar 07 2017

%Y Cf. A019565 (base 2), A101278 (base 3), A101942 (base 4), A054842 (base 10).

%K base,nonn,easy

%O 0,2

%A Orges Leka (oleka(AT)students.uni-mainz.de), Dec 21 2004