A337448 -id:A337448 - cp's OEIS frontend

A117774 Fibonacci numbers which are divisible by the sum of their digits.

1, 2, 3, 5, 8, 21, 144, 2584, 14930352, 86267571272, 498454011879264, 160500643816367088, 114059301025943970552219, 5358359254990966640871840, 555565404224292694404015791808, 1226132595394188293000174702095995, 18547707689471986212190138521399707760

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Intersection of A005349 and A000045. - Michel Marcus, Jul 11 2016

			2584 is in the sequence because (1) it is a Fibonacci number, (2) the sum of its digits is 2+5+8+4=19 and 2584 is divisible by 19.

Harvey P. Dale, Table of n, a(n) for n = 1..64

Cf. A000045, A005349, A337448.

with(combinat): a:=proc(n) local ff, sod: ff:=convert(fibonacci(n),base,10): sod:=add(ff[j],j=1..nops(ff)): if type(fibonacci(n)/sod,integer)=true then fibonacci(n) else fi end: seq(a(n),n=2..180); # Emeric Deutsch, Apr 16 2006

Select[Fibonacci[Range[2,250]],Divisible[#,Total[IntegerDigits[#]]]&] (* Harvey P. Dale, May 06 2013 *)

{m=170; for(n=2,m,a=fibonacci(n); s=0; k=a; while(k>0, d=divrem(k,10); k=d[1]; s=s+d[2]); if(a%s==0,print1(a,",")))} \\ Klaus Brockhaus, Apr 16 2006

a(11) to a(16) from Emeric Deutsch and Klaus Brockhaus, Apr 16 2006

a(17) from Harvey P. Dale, May 06 2013

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

Original entry on oeis.org

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

Marius A. Burtea, Sep 14 2020

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.

			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.

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

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

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

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

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

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

A353988 Numbers k such that Fibonacci(k) is a binary Niven number (A049445).

Original entry on oeis.org

1, 2, 3, 6, 8, 9, 10, 12, 18, 24, 30, 36, 48, 56, 60, 100, 120, 144, 150, 168, 240, 270, 288, 300, 324, 330, 336, 360, 444, 540, 594, 600, 624, 720, 750, 840, 864, 896, 900, 936, 1080, 1152, 1200, 1210, 1360, 1404, 1632, 1720, 1921, 2028, 2400, 2520, 2552, 2864

Offset: 1

Amiram Eldar, May 13 2022

Numbers k such that A011373(k) | A000045(k).

			1 is a term since A000045(1) = A011373(1) = 1 and 1 | 1.
10 is a term since A000045(10) = 55, A011373(1) = 5 and 5 | 55.

Amiram Eldar, Table of n, a(n) for n = 1..3000

Cf. A000045, A000120, A011373, A049445, A117774, A337448 (decimal analog).

Select[Range[3000], Divisible[(f = Fibonacci[#]), DigitCount[f, 2, 1]] &]

isok(k) = my(f=fibonacci(k)); ! (f % hammingweight(f)); \\ Michel Marcus, May 13 2022

cp's OEIS Frontend

A117774 Fibonacci numbers which are divisible by the sum of their digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A353988 Numbers k such that Fibonacci(k) is a binary Niven number (A049445).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI