A335708 a(n) is the number of divisors of the n-th Niven number.

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 6, 6, 6, 4, 8, 4, 8, 9, 8, 8, 6, 10, 6, 8, 12, 6, 8, 12, 10, 5, 12, 12, 9, 8, 12, 8, 4, 10, 8, 6, 16, 12, 12, 4, 8, 12, 15, 12, 8, 6, 12, 10, 6, 18, 8, 14, 8, 12, 12, 4, 12, 6, 4, 16, 16, 12, 8, 12, 9, 12, 8, 12, 20, 6, 4, 18, 6, 16

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Formula

a(n) = A000005(A005349(n)).

Example

The first Niven number is 1 and tau(1) = 1, so a(1) = 1.
The second Niven number is 2 and tau(2) = 2, so a(2) = 2.
The 11th Niven number is 12 and tau(12) = 6, so a(11) = 6.

Mathematica

DivisorSigma[0, Select[Range[265], Divisible[#, Plus @@ IntegerDigits[#]] &]] (* Amiram Eldar, Aug 04 2020 *)

Prog

(Magma) niven:=func<n|n mod &+Intseq(n) eq 0 >; [#Divisors(k):k in [1..300]|niven(k)];

Crossrefs

Cf. A000005, A005349, A007953.

Sequence in context: A218704 A144373 A086292 * A076640 A326198 A324105

Adjacent sequences: A335705 A335706 A335707 * A335709 A335710 A335711

Keyword

nonn,base

Author

Marius A. Burtea, Aug 04 2020

Status

approved