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A080367
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Largest unitary prime divisor of n or a(n)=0 if no such prime-divisor exists.
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1
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| See [Grah, Section 5] for growth rate of the partial sums. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 03 2009]
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LINKS
| J. Grah, Comportement moyen du cardinal de certains ensembles de facteurs premiers, Monatsh. Math. 118 (1994) 91-109. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 03 2009]
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EXAMPLE
| n=252100=2.2.3.5.5.7.11.11, unitary prime divisors={3,7}; largest is 7, so a(252100)=7
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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}]
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CROSSREFS
| Cf. A034444, A056169.
Sequence in context: A080368 A057174 A199514 * A066913 A090303 A051444
Adjacent sequences: A080364 A080365 A080366 * A080368 A080369 A080370
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KEYWORD
| nonn
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AUTHOR
| Labos E (labos(AT)ana.sote.hu), Feb 21 2003
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