A356349 Primitive Niven numbers: terms of A005349 that are not ten times another term of A005349.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 18, 21, 24, 27, 36, 42, 45, 48, 54, 63, 72, 81, 84, 102, 108, 110, 111, 112, 114, 117, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 190, 192, 195, 198, 201, 204, 207, 209, 216, 220, 222, 224, 225, 228, 230, 234

Offset: 1

Author

Bernard Schott and Rémy Sigrist, Oct 15 2022

Keywords

• nonn
• base
• easy

Comments

A005349(k) belongs to this sequence iff A113315(k) is not a multiple of 10.

This sequence is infinite as it contains A133384 and A199682.

Each Niven number can be uniquely written as a(m)*10^z for some m > 0 and z >= 0.

This sequence contains numbers with k trailing zeros for any k >= 0; for example R(2^k) * 10^k (where R = A002275).

Examples

			190 is a term as 190 is a Niven number and 19 is not a Niven number.
192 is a term as 192 is a Niven number and 192 is not divisible by 10.
		

Links

• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A002275, A005349, A113315, A133384, A199682.

Programs

PARI

is(n, base=10) = my (s=sumdigits(n, base)); n%s==0 && (n%base || (n/base)%s)

Python

def ok(n):
    sd = sum(map(int, str(n)))
    return sd and not n%sd and (n%10 or (n//10)%sd)
print([k for k in range(235) if ok(k)]) # Michael S. Branicky, Oct 16 2022