A225298 Smallest pandigital number with exactly n prime factors (with multiplicity).

10123457689, 10123456789, 1023456879, 1023456987, 1023456897, 1023456789, 1023456798, 1023457896, 1023486975, 1023479856, 1023458976, 1023475968, 1024973568, 1023579648, 1024897536, 1023657984, 1032984576, 1034698752, 1093865472, 1074659328, 1072963584

Offset: 1

Author

Jonathan Vos Post, May 04 2013

Keywords

• nonn
• base
• easy

Comments

Smallest pandigital n-almost prime.

Examples

			a(1) = 10123457689 is the least prime pandigital number (A221646), that is, the smallest prime containing all the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
a(2) = 10123456789 = 919 * 11015731, the smallest pandigital semiprime.
a(3) = 1023456879, the smallest pandigital number (A171102) that is 3-almost prime (product of three primes with repetition).
a(4) = 1023456987 = 3^2 * 7 * 16245349, which is the smallest pandigital 4-almost prime.
a(5) = 1023456897 = 3^3 * 2417 * 15683.
a(6) = 1023456789 = 3^4 * 2221 * 5689.
a(7) = 1023456798 = 2 * 3^2 * 7 * 13 * 487 * 1283.
a(8) = 1023457896 = 2^3 * 3^3 * 59 * 80309.
		

Crossrefs

Cf. A171102, A221646, A175845.

Programs

Mathematica

a[n_] := Block[{k = If[n < 3, 10123456789, 1023456789]}, While[ Union@ IntegerDigits@ k != Range[0, 9] || Total[Last /@ FactorInteger[k]] != n, k++]; k]; Array[a, 10] (* Giovanni Resta, May 06 2013 *)

Formula

a(n) = MIN{k such that k is in A050278 and bigomega(k) = n}.

a(n) = MIN{k such that k is in A050278 and A001222(k) = n}.

Extensions

a(2) corrected and a(9)-a(21) from Giovanni Resta, May 06 2013