A379930 Numbers that have the same number of divisors as there are runs in their base-10 representation.

1, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 121, 169, 199, 211, 223, 227, 229, 233, 277, 289, 311, 331, 337, 361, 433, 443, 449, 499, 529, 557, 577, 599, 661, 677, 733, 773, 811, 841, 877, 881, 883, 887, 911, 961, 977, 991, 997, 1018, 1027, 1037, 1041

Offset: 1

Author

Robert Israel, Jan 06 2025

Keywords

• nonn
• base

Comments

Numbers k such that A000005(k) = A043562(k).

Examples

			a(5) = 23 is a term because it has two runs, 2 and 3, and two divisors, 1 and 23.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A043562, A379929, A379931.

Programs

Maple

filter:= proc(n) local L; L:= convert(n, base, 10); nops(L) - numboccur(0, L[2..-1]-L[1..-2]) = numtheory:-tau(n) end proc:
select(filter, [$1..1000]);

Mathematica

A379930Q[n_] := DivisorSigma[0, n] == Length[Split[IntegerDigits[n]]];
Select[Range[1000], A379930Q] (* Paolo Xausa, Jan 08 2025 *)