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A117774
Fibonacci numbers which are divisible by the sum of their digits.
4
1, 2, 3, 5, 8, 21, 144, 2584, 14930352, 86267571272, 498454011879264, 160500643816367088, 114059301025943970552219, 5358359254990966640871840, 555565404224292694404015791808, 1226132595394188293000174702095995, 18547707689471986212190138521399707760
OFFSET
1,2
COMMENTS
Intersection of A005349 and A000045. - Michel Marcus, Jul 11 2016
LINKS
EXAMPLE
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.
MAPLE
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
MATHEMATICA
Select[Fibonacci[Range[2, 250]], Divisible[#, Total[IntegerDigits[#]]]&] (* Harvey P. Dale, May 06 2013 *)
PROG
(PARI) {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
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006
EXTENSIONS
a(11) to a(16) from Emeric Deutsch and Klaus Brockhaus, Apr 16 2006
a(17) from Harvey P. Dale, May 06 2013
STATUS
approved