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

1,2

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

Links

Table of n, a(n) for n=1..24.

Prog

(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

Crossrefs

Cf. A076961.

Sequence in context: A224873 A085836 A073916 * A370416 A304480 A129599

Adjacent sequences: A076959 A076960 A076961 * A076963 A076964 A076965

Keyword

nonn

Author

Amarnath Murthy, Oct 21 2002

Extensions

Corrected and extended by Sascha Kurz, Jan 22 2003

More terms from Michel Marcus, Mar 19 2013

Status

approved