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%I #12 Mar 15 2017 12:23:18
%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
%N Sequence f[n,4], where f[n,b] is as defined below.
%F Let n = Sum[b^(i-1) * c_{i}] where 1 <= i <=r of N, c_{r}!=0, n of N, c_{i} of {0, 1, ..., b-2, b-1}. Then f[n, b] := Product[prime(i)^c_{i}]] 1 <= i <= r. Formula: For all b>=2, k of N_{0} : f[b^k, b] = prime(k-1).
%e f[29,4] = 270 because 29 = 131_4 -> f[29,4] = 5^1 * 3^3 * 2^1;
%e f[5,2] = 10 because 5 = 101_2 -> f[5,2] = 5^1 * 3^0 * 2^1;
%e f[5,3] = 12 because 5 = 12_3 -> f[5,3] = 3^1 * 2^2;
%e f[0,b] = 1 because 0 = 0_b -> f[0,b] = 2^0.
%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 A060882 = f[2^n - 1, 2] - f[2^n, 2].
%K base,nonn
%O 0,2
%A Orges Leka (oleka(AT)students.uni-mainz.de), Dec 21 2004
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