OFFSET
1,2
COMMENTS
See [Grah, Section 5] for growth rate of the partial sums. - R. J. Mathar, Mar 03 2009
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Jacques Grah, Comportement moyen du cardinal de certains ensembles de facteurs premiers, Monatsh. Math. 118 (1994) 91-109. [From R. J. Mathar, Mar 03 2009]
FORMULA
from Amiram Eldar, Aug 17 2024: (Start)
a(n) = 0 if and only of n is powerful (A001694).
EXAMPLE
For n = 252100 = 2*2*3*5*5*7*11*11, the unitary prime divisors are {3,7}, the largest is 7, so a(252100) = 7.
MATHEMATICA
ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; gb[x_] := GCD[ba[x], x/ba[x]]; fpg[x_] := Flatten[Position[gb[x], 1]]; upd[x_] := Part[ba[x], fpg[x]]; mxu[x_] := Max[upd[x]]; miu[x_] := Min[upd[x]]; Do[If[Equal[upd[n], {}], Print[0]]; If[ !Equal[upd[n], {}], Print[mxu[n]]], {n, 2, 256}]
a[n_] := Max[Join[Select[FactorInteger[n], Last[#] == 1 &][[;; , 1]], {0}]]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Aug 17 2024 *)
PROG
(Haskell)
a080367 n = if null us then 0 else fst $ last us
where us = filter ((== 1) . snd) $ zip (a027748_row n) (a124010_row n)
-- Reinhard Zumkeller, Jul 23 2014
(PARI) a(n) = {my(f = factor(n), pmax = 0); for(i = 1, #f~, if(f[i, 2] == 1 && f[i, 1] > pmax, pmax = f[i, 1])); pmax; } \\ Amiram Eldar, Aug 17 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Feb 21 2003
STATUS
approved