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A034708
Numbers for which the sum of reciprocals of digits is an integer.
10
1, 11, 22, 111, 122, 212, 221, 236, 244, 263, 326, 333, 362, 424, 442, 623, 632, 1111, 1122, 1212, 1221, 1236, 1244, 1263, 1326, 1333, 1362, 1424, 1442, 1623, 1632, 2112, 2121, 2136, 2144, 2163, 2211, 2222, 2316, 2361, 2414, 2441, 2488, 2613, 2631, 2666
OFFSET
1,2
COMMENTS
Intersection of A214957 and A052382: A214950(a(n))*A168046(a(n)) = 1. - Reinhard Zumkeller, Aug 02 2012
LINKS
MATHEMATICA
f[ n_ ] := 1/n a[ n_ ] := Apply[ Plus, Map[ f, IntegerDigits[ n ] ] ] Select[ Range[ 1000 ], FreeQ[ IntegerDigits[ # ], 0 ] && IntegerQ[ a [ # ] ] & ] (* Santi Spadaro, Oct 13 2001 *)
Select[Range[3000], DigitCount[#, 10, 0]==0 && IntegerQ[Total[ 1/IntegerDigits[#]]]&] (* Harvey P. Dale, May 06 2012 *)
PROG
(Haskell)
a034708 n = a034708_list !! (n-1)
a034708_list = filter ((== 1) . a168046) a214957_list
-- Reinhard Zumkeller, Aug 02 2012
(PARI) isok(n) = {my(d = digits(n)); vecmin(d) && denominator(sum(k=1, #d, 1/d[k])) == 1; } \\ Michel Marcus, Feb 12 2016
(Python)
from fractions import Fraction
def srd(n): return sum(Fraction(1, int(d)) for d in str(n)) # assumes no 0's
def ok(n): return False if '0' in str(n) else srd(n).denominator == 1
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(2666)) # Michael S. Branicky, Jan 11 2021
CROSSREFS
KEYWORD
nonn,base,nice
STATUS
approved