A085629 Let b(n) equal the product of the exponents in the prime factorization of n. Then a(n) gives the least k such that b(k) = n.

1, 4, 8, 16, 32, 64, 128, 144, 216, 288, 2048, 432, 8192, 1152, 864, 1296, 131072, 1728, 524288, 2592, 3456, 18432, 8388608, 5184, 7776, 73728, 13824, 10368, 536870912, 15552, 2147483648, 20736, 55296, 1179648, 31104, 41472, 137438953472, 4718592

Offset: 1

Author

Jason Earls, Jul 10 2003

Keywords

• nonn

Comments

a(n) <= 2^n. - Robert G. Wilson v, Jul 14 2014

a(n) = 2^n iff n is a prime or n equals 4 or 6. - Robert G. Wilson v, Jul 19 2014

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A005361, A005934.

Cf. A005179.

Subsequence of A181800.

Programs

Mathematica

f[n_, i_] := f[n, i] = Block[{d, b, p, x}, p = Prime[i]; b = p^n; d = Divisors[n]; For[j = Length[d], j > 1, j--, x = d[[j]]; b = Min[b, p^x*f[n/x, i + 1]]]; b]; f[1, 1] = 1; Array[ f[#, 1] &, 42] (* Robert G. Wilson v, Jul 17 2014, after David Wasserman's PARI program below *)

PARI

f(n, i) = local(d, best, p, x); p = prime(i); best = p^n; d = divisors(n); for (j = 2, length(d) - 1, x = d[j]; best = min(best, p^x*f(n/x, i + 1))); best; a(n) = f(n, 1) \\ David Wasserman, Feb 07 2005

Extensions

More terms from David Wasserman, Feb 07 2005