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

1,2

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

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 *)

Crossrefs

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

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

Sequence in context: A120533 A226108 A273906 * A125845 A108871 A347819

Adjacent sequences: A095859 A095860 A095861 * A095863 A095864 A095865

Keyword

base,nonn

Author

Ray Chandler, Jun 28 2004

Extensions

Edited by M. F. Hasler, Nov 29 2007

Status

approved