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

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, 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, 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

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

J. Grah, Comportement moyen du cardinal de certains ensembles de facteurs premiers, Monatsh. Math. 118 (1994) 91-109. [From R. J. Mathar, Mar 03 2009]

Example

n = 252100 = 2*2*3*5*5*7*11*11, unitary prime divisors = {3,7}; 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}]

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

Crossrefs

Cf. A034444, A056169, A080368.

Cf. A027748, A124010.

Sequence in context: A057174 A197658 A199514 * A354365 A066913 A090303

Adjacent sequences: A080364 A080365 A080366 * A080368 A080369 A080370

Keyword

nonn

Author

Labos Elemer, Feb 21 2003

Status

approved