A108871 Numbers n such that the number of digits required to write the prime factors of n is equal to the number of divisors of n.

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 143, 187, 202, 206, 209, 214, 218, 221, 226, 247, 253, 254, 262, 274, 278, 298, 299, 302, 303, 309, 314, 319, 321, 323, 326, 327, 334, 339, 341, 346, 358, 362, 377, 381, 382, 386

Offset: 1

Author

Jason Earls, Jul 13 2005

Keywords

• base
• easy
• nonn

Comments

190333 has 10 divisors and 10 digits in its prime factorization. What is the next term in this sequence with more divisors and digits?

2093663 has 12 divisors and 12 digits in its prime factorization. - Harvey P. Dale, Apr 05 2019

Prime factors are counted with multiplicity. - Harvey P. Dale, Apr 05 2019

Examples

			143 is a term because it takes 4 digits to write its prime factorization
143=11*13 and has 4 divisors [1, 11, 13, 143].
		

Crossrefs

Cf. A076649.

Programs

Mathematica

ndQ[n_]:=Total[#[[2]]IntegerLength[#[[1]]]&/@FactorInteger[n]] == DivisorSigma[ 0,n]; Select[Range[2,500],ndQ]