a(n) = smallest k such that k*n is a Niven (or Harshad) number.

[Davide Rotondo]

Hi everyone, today I was checking https://oeis.org/A144261 and I noticed that the larger a(n) = the smallest k such that k*n is a Niven (or Harshad) number, the higher the probability that n is a prime number.

What do you think?

See you soon

Davide

[Davide Rotondo]

For example, taking into consideration the numbers such that a(n)>=9 i have:

11,13,23,29,31,41,43,47,53,58,59,61,71,79,83,89,94,97,101,103,106,107,109,113,116,118,131,137,139,142,149,151,157,158,166,173,...

up to 299 the numbers not prime that have this property are only even.

The first odd number with this property is 299.

See you soon 

Davide

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[M F Hasler]

On Thu, Sep 25, 2025 at 5:11 AM Davide Rotondo <david...@gmail.com> wrote:

Hi everyone, today I was checking https://oeis.org/A144261 and I noticed that the larger a(n) = the smallest k such that k*n is a Niven (or Harshad) number, the higher the probability that n is a prime number.

What do you think?

If you have a sequence

a(n) = least k such that Property(kn)

what can you say about

a(mq) with respect to a(q) and a(m) ?

-M.

[Davide Rotondo]

Sorry I don't understand.

Davide

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