A337449 The numbers k for which Lucas(k) are Niven numbers.

0, 1, 2, 3, 4, 6, 12, 18, 56, 81, 130, 225, 396, 637, 854, 2034, 4059, 4095, 5985, 7650, 21105, 31059, 41998, 46860, 83106, 114129, 120555, 150705, 201285, 287937, 338265, 359757, 475839, 512194, 583825, 606594, 627102, 717025, 877305, 922095, 991590, 1076355

Offset: 1

Author

Marius A. Burtea, Sep 14 2020

Keywords

• nonn
• base

Comments

For a(6) = 6, Lucas(6) = 18 and 18/digsum(18) = 2 is a prime number, so Lucas(6) is a Moran number (A001101).

For a(9) = 56, Lucas(56) = 505019158607 and 505019158607/digsum(505019158607) = 10745088481 is a prime number, so Lucas(56) is a Moran number.

Examples

			Lucas(0) = 2 = A005349(2), so 0 is a term.
Lucas(1) = 1 = A005349(1), so 1 is a term.
Lucas(6) = 12 = A005349(11), so 6 is a term.
Lucas(12) = 322 = A005349(90), so 12 is a term.
Lucas(18) = 5778 = A005349(1013), so 18 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..57

Crossrefs

Cf. A000032, A139374, A001101, A005349, A337448.

Programs

Magma

niven:=func; [k:k in [0..70000]|niven(Lucas(k))];

Mathematica

nivenQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; Select[Range[6000], nivenQ[LucasL[#]] &] (* Amiram Eldar, Sep 15 2020 *)

PARI

isok(k) = my(l=real((2+quadgen(5))*quadgen(5)^k)); (l % sumdigits(l)) == 0; \\ Michel Marcus, Sep 15 2020

Python

A337449_list, k, p, q = [], 0, 2, 1
while k < 10**6:
    if p % sum(int(d) for d in str(p)) == 0:
        A337449_list.append(k)
    k += 1
    p, q = q, p+q # Chai Wah Wu, Sep 17 2020