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A080367 Largest unitary prime divisor of n or a(n)=0 if no such prime divisor exists. 2

%I #16 Sep 04 2017 21:29:05

%S 0,2,3,0,5,3,7,0,0,5,11,3,13,7,5,0,17,2,19,5,7,11,23,3,0,13,0,7,29,5,

%T 31,0,11,17,7,0,37,19,13,5,41,7,43,11,5,23,47,3,0,2,17,13,53,2,11,7,

%U 19,29,59,5,61,31,7,0,13,11,67,17,23,7,71,0,73,37,3,19,11,13,79,5,0,41,83,7

%N Largest unitary prime divisor of n or a(n)=0 if no such prime divisor exists.

%C See [Grah, Section 5] for growth rate of the partial sums. [_R. J. Mathar_, Mar 03 2009]

%H Reinhard Zumkeller, <a href="/A080367/b080367.txt">Table of n, a(n) for n = 1..10000</a>

%H J. Grah, <a href="http://dx.doi.org/10.1007/BF01305777">Comportement moyen du cardinal de certains ensembles de facteurs premiers</a>, Monatsh. Math. 118 (1994) 91-109. [From _R. J. Mathar_, Mar 03 2009]

%e n = 252100 = 2*2*3*5*5*7*11*11, unitary prime divisors = {3,7}; largest is 7, so a(252100)=7.

%t 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}]

%o (Haskell)

%o a080367 n = if null us then 0 else fst $ last us

%o where us = filter ((== 1) . snd) $ zip (a027748_row n) (a124010_row n)

%o -- _Reinhard Zumkeller_, Jul 23 2014

%Y Cf. A034444, A056169, A080368.

%Y Cf. A027748, A124010.

%K nonn

%O 1,2

%A _Labos Elemer_, Feb 21 2003

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