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

1,2

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).

Links

Table of n, a(n) for n=1..58.

Index entries for sequences related to decimal expansion of n

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A079238 A079042 A193455 * A343680 A114440 A334416

Adjacent sequences: A356346 A356347 A356348 * A356350 A356351 A356352

Keyword

nonn,base,easy

Author

Bernard Schott and Rémy Sigrist, Oct 15 2022

Status

approved