OFFSET
1,2
COMMENTS
The prime 479 first appears in f(m) at m = 2395, ahead of 71, which first appears in f(2485).
The first occurrence of four distinct primes is at m = 2500, with 5^7, 17^3, 71 and 479.
For 1890 < m < 2006, d(m) is a square (f(m)=1). The lone prime in 1875 .. 1890 is 61 and in 2006 .. 2027 it is 59.
It appears that f(m) can differ from f(m-1) in at most one prime.
(f from definition) = A007913, squarefree part. - Reinhard Zumkeller, Jul 06 2012
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..250
EXAMPLE
f(10) = 5 is the first time f(m) > 1. The 5 persists until it disappears at m = 15.
MATHEMATICA
d[n_] := Denominator[ HarmonicNumber[n, 2]]; f[n_] := Times @@ Select[ FactorInteger[d[n]], OddQ[#[[2]]]&][[All, 1]]; A035166 = Join[{1}, Select[ Range[1000], f[#] != f[#-1]&]] (* Jean-François Alcover, Feb 26 2016 *)
PROG
(Macsyma) for k:1 do (subset(factor_number(denom(harmonic(k, 2))), lambda([x], oddp(second(x)))), if old#old:%% then print(k, %%))
(Haskell)
import Data.List (findIndices)
a035166 n = a035166_list !! (n-1)
a035166_list = map (+ 1) $ findIndices (/= 0) $ zipWith (-) (tail gs) gs
where gs = 0 : map a007913 a007407_list
-- Reinhard Zumkeller, Jul 06 2012
(PARI) d(m) = denominator(sum(k=1, m, 1/k^2));
f(m) = my(f=factor(d(m))); for (k=1, #f~, if (!(f[k, 2] % 2), f[k, 2] = 0)); factorback(f);
isok(m) = if (m==1, 1, f(m) != f(m-1)); \\ Michel Marcus, Sep 06 2023
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Bill Gosper, Sep 04 2002
STATUS
approved