A095862 Numbers whose number of decimal digits and number of divisors are equal.

1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 121, 169, 289, 361, 529, 841, 961, 1003, 1006, 1007, 1011, 1018, 1027, 1037, 1041, 1042, 1043, 1046, 1047, 1055, 1057, 1059, 1067, 1073, 1077, 1079, 1081, 1082, 1094, 1099

Offset: 1

Author

Ray Chandler, Jun 28 2004

Keywords

• base
• nonn

Comments

An element of this sequence is prime iff it has 2 digits, which is the case for a(2)=11 through a(22); sequence A096489 lists exactly these and the leading term a(1)=1 (the only noncomposite number which is not prime). - M. F. Hasler, Nov 29 2007

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096489 (= a(1)..a(22) = noncomposite elements of this sequence).

Cf. A135772-A135779 (analog for bases 2...9).

Programs

Maple

q:= n-> is(length(n)=numtheory[tau](n)):
select(q, [$1..1100])[];  # Alois P. Heinz, Jun 18 2021

Mathematica

Select[Range[1100],IntegerLength[#]==DivisorSigma[0,#]&] (* Harvey P. Dale, Oct 19 2015 *)

Extensions

Edited by M. F. Hasler, Nov 29 2007