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A061299 Least number whose number of divisors is A007304(n) (the n-th number that is the product of 3 distinct primes). 7
720, 2880, 46080, 25920, 184320, 2949120, 129600, 414720, 11796480, 1658880, 188743680, 3732480, 2073600, 26542080, 12079595520, 14929920, 48318382080, 106168320, 8294400, 3092376453120, 1698693120, 18662400, 238878720 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..23.

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

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

AUTHOR

Labos Elemer, Jun 05 2001

EXTENSIONS

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

STATUS

approved

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Last modified April 20 05:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)