A061299 - OEIS

%I #27 Feb 04 2025 07:16:59

%S 720,2880,46080,25920,184320,2949120,129600,414720,11796480,1658880,

%T 188743680,3732480,2073600,26542080,12079595520,14929920,48318382080,

%U 106168320,8294400,3092376453120,1698693120,18662400,238878720

%N Least number whose number of divisors is A007304(n) (the n-th number that is the product of 3 distinct primes).

%C All terms are divisible by a(1) = 720, the first entry.

%C All terms [=a(j)], not only arguments [=j] have 3 distinct prime factors at exponents determined by the p,q,r factors of their arguments: a(pqr) = RPQ.

%H Amiram Eldar, <a href="/A061299/b061299.txt">Table of n, a(n) for n = 1..3706</a> (terms 1..835 from David A. Corneth)

%F a(n) = A005179(A007304(n)).

%F Min{x; A000005(x) = pqr} p, q, r are distinct primes. If k = pqr and p > q > r then A005179(k) = 2^(p-1)*3^(q-1)*5^(r-1).

%F From _Reinhard Zumkeller_, Jul 15 2004: (Start)

%F A000005(a(n)) = A007304(n).

%F A000005(m) != A007304(n) for m < a(n).

%F a(n) = A005179(A007304(n)).

%F a(p*m*q) = 2^(q-1) * 3^(m-1) * 5^(p-1) for primes p < m < q.

%F a(A000040(i)*A000040(j)*A000040(k)) = 2^(A084127(k)-1) * 3^(A084127(j)-1) * 5^(A084127(i)-1) for i < j < k. (End)

%e For n = 5: A007304(5) = 78 = 2*3*13, A005179(78) = 184320 = (2^12)*(3^2)*(5^1) = a(5).

%Y Cf. A000005, A005179, A007304, A061148, A061149.

%Y Cf. A096932, A061234, A061286.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 05 2001

%E Edited by _N. J. A. Sloane_, Apr 20 2007