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A076745
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a(n) = the least positive integer k such that b(k) = n, where b(k) (A076526) is defined by b(k) = r * max{e_1,...,e_r} if k = p_1^e_1 *...* p_r^e_r is the canonical prime factorization of k.
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2
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2, 4, 8, 12, 32, 24, 128, 48, 120, 96, 2048, 192, 8192, 384, 480, 768, 131072, 960, 524288, 3072, 1920, 6144, 8388608, 3840, 36960, 24576, 7680, 13440, 536870912, 15360, 2147483648, 26880, 30720, 393216, 147840, 53760, 137438953472, 1572864, 122880, 107520, 2199023255552
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = Min_{d|n} (2^d * Product_{i=1..n/d-1} prime(i+1)).
a(p) = 2^p for a prime p.
a(2*p) = 3*2^p for a prime p.
a(3*p) = 15*2^p for a prime p > 2. (End)
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EXAMPLE
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a(12) = 2 * max{1,2} = 4 since 12 = 2^2 * 3^1 and 12 is the least k for which b(k) = 4. Hence a(4) = 12.
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MATHEMATICA
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a[n_] := Min[Table[2^d*Times @@ Prime[Range[2, n/d]], {d, Divisors[n]}]]; Array[a, 50] (* Amiram Eldar, Sep 08 2024 *)
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PROG
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(PARI) a(n) = {my(f = factor(n), nd = numdiv(f), v = vector(nd), k = 0); fordiv(f, d, k++; v[k] = 2^d * prod(i = 1, n/d-1, prime(i+1))); vecmin(v); } \\ Amiram Eldar, Sep 08 2024
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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