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A076745 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.

%I A076745 #12 Sep 09 2024 09:34:53
%S A076745 2,4,8,12,32,24,128,48,120,96,2048,192,8192,384,480,768,131072,960,
%T A076745 524288,3072,1920,6144,8388608,3840,36960,24576,7680,13440,536870912,
%U A076745 15360,2147483648,26880,30720,393216,147840,53760,137438953472,1572864,122880,107520,2199023255552
%N A076745 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.
%H A076745 Amiram Eldar, <a href="/A076745/b076745.txt">Table of n, a(n) for n = 1..1000</a>
%H A076745 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_201.htm">Puzzle 201: The Arithmetic Function A(n)</a>, The Prime Puzzles and Problems Connection.
%F A076745 From _Amiram Eldar_, Sep 08 2024: (Start)
%F A076745 a(n) = Min_{d|n} (2^d * Product_{i=1..n/d-1} prime(i+1)).
%F A076745 a(p) = 2^p for a prime p.
%F A076745 a(2*p) = 3*2^p for a prime p.
%F A076745 a(3*p) = 15*2^p for a prime p > 2. (End)
%e A076745 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.
%t A076745 a[n_] := Min[Table[2^d*Times @@ Prime[Range[2, n/d]], {d, Divisors[n]}]]; Array[a, 50] (* _Amiram Eldar_, Sep 08 2024 *)
%o A076745 (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
%Y A076745 Cf. A076526.
%K A076745 nonn,easy
%O A076745 1,1
%A A076745 _Joseph L. Pe_, Nov 11 2002
%E A076745 More terms from _Amiram Eldar_, Sep 08 2024