OFFSET
1,1
COMMENTS
If x' = n has solutions, they occur for x <= (n/2)^2. - T. D. Noe, Oct 12 2004
A099302(a(n)) = 0. - Reinhard Zumkeller, Mar 18 2014
LINKS
T. D. Noe, Table of n, a(n) for n = 1..5000
Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003. (See p. 7.)
MATHEMATICA
a[1] = 0; a[n_] := Block[{f = Transpose[ FactorInteger[ n]]}, If[ PrimeQ[n], 1, Plus @@ (n*f[[2]]/f[[1]])]]; b = Table[ -1, {500}]; b[[1]] = 1; Do[c = a[n]; If[c < 500 && b[[c + 1]] == 0, b[[c + 1]] = n], {n, 10^6}]; Select[ Range[500], b[[ # ]] == 0 &]
dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; d1=Table[dn[n], {n, 40000}]; Select[Range[400], 0==Count[d1, # ]&]
PROG
(Haskell)
a098700 n = a098700_list !! (n-1)
a098700_list = filter
(\z -> all (/= z) $ map a003415 [1 .. a002620 z]) [2..]
-- Reinhard Zumkeller, Mar 18 2014
(PARI) list(lim)=my(v=List()); lim\=1; forfactored(n=1, lim^2, my(f=n[2], t); listput(v, n[1]*sum(i=1, #f~, f[i, 2]/f[i, 1]))); setminus([1..lim], Set(v)); \\ Charles R Greathouse IV, Oct 21 2021
(Python)
from itertools import count, islice
from sympy import factorint
def A098700_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda n:all(map(lambda m:sum((m*e//p for p, e in factorint(m).items())) != n, range(1, (n**2>>1)+1))), count(max(startvalue, 2)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 21 2004
EXTENSIONS
Corrected and extended by T. D. Noe, Oct 12 2004
STATUS
approved