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A080367 Largest unitary prime divisor of n or a(n)=0 if no such prime divisor exists. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 30 06:00 EDT 2022. Contains 354914 sequences. (Running on oeis4.)