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

1,1

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

Links

Table of n, a(n) for n=1..57.

Example

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].

Mathematica

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

Crossrefs

Cf. A076649.

Sequence in context: A273906 A095862 A125845 * A347819 A268031 A167847

Adjacent sequences: A108868 A108869 A108870 * A108872 A108873 A108874

Keyword

base,easy,nonn

Author

Jason Earls, Jul 13 2005

Status

approved