A076962 Smallest multiple of prime(n) with n divisors, or 0 if no such number exists.

0, 3, 25, 14, 14641, 52, 24137569, 114, 2116, 464, 819628286980801, 444, 22563490300366186081, 2752, 35344, 1272, 21559177407076402401757871041, 2196, 740195513856780056217081017732809, 3408, 341056, 80896, 1658509762573818415340429240403156732495289, 5340

Offset: 1

Author

Amarnath Murthy, Oct 21 2002

Keywords

• nonn

Comments

If p is a prime then a(p) = prime(p)^(p-1).

No entry is zero for n>1, since prime(n)^(n-1) has exactly n divisors. When n is not prime, this will generally be greater than a(n), but it suffices to prove existence. - Franklin T. Adams-Watters, May 14 2014

Crossrefs

Cf. A076961.

Programs

PARI

a(n) = {if (n==1, return (0)); if (isprime(n), return (prime(n)^(n-1))); np = prime(n); mnp = np; while (numdiv(mnp) != n, mnp += np;); return (mnp);}  \\ Michel Marcus, Mar 19 2013

Extensions

Corrected and extended by Sascha Kurz, Jan 22 2003

More terms from Michel Marcus, Mar 19 2013