A061299 Least number whose number of divisors is A007304(n) (the n-th number that is the product of 3 distinct primes).

720, 2880, 46080, 25920, 184320, 2949120, 129600, 414720, 11796480, 1658880, 188743680, 3732480, 2073600, 26542080, 12079595520, 14929920, 48318382080, 106168320, 8294400, 3092376453120, 1698693120, 18662400, 238878720

Offset

1,1

Comments

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

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..3706 (terms 1..835 from David A. Corneth)

Formula

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

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).

From Reinhard Zumkeller, Jul 15 2004: (Start)

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

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

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

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

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

Example

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

Crossrefs

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

Cf. A096932, A061234, A061286.

Sequence in context: A052794 A226885 A096933 * A167563 A202095 A233787

Adjacent sequences: A061296 A061297 A061298 * A061300 A061301 A061302

Keyword

nonn,changed

Author

Labos Elemer, Jun 05 2001

Extensions

Edited by N. J. A. Sloane, Apr 20 2007

Status

approved