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A080368
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a(n) is the least unitary prime divisor of n, or 0 if no such prime divisor exists.
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4
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0, 2, 3, 0, 5, 2, 7, 0, 0, 2, 11, 3, 13, 2, 3, 0, 17, 2, 19, 5, 3, 2, 23, 3, 0, 2, 0, 7, 29, 2, 31, 0, 3, 2, 5, 0, 37, 2, 3, 5, 41, 2, 43, 11, 5, 2, 47, 3, 0, 2, 3, 13, 53, 2, 5, 7, 3, 2, 59, 3, 61, 2, 7, 0, 5, 2, 67, 17, 3, 2, 71, 0, 73, 2, 3, 19, 7, 2, 79, 5, 0, 2, 83, 3, 5, 2, 3, 11, 89, 2, 7, 23, 3, 2
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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n = 252100 = 2*2*3*5*5*7*11*11, unitary prime divisors = {3,7}; smallest is 3, so a(252100)=3.
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MATHEMATICA
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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[miu[n]]], {n, 2, 256}]
Table[If[Or[n == 1, Length@ # == 0], 0, First@ #] &@ Select[FactorInteger[n][[All, 1]], GCD[#, n/#] == 1 &], {n, 94}] (* Michael De Vlieger, Oct 30 2016 *)
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PROG
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(Haskell)
a080368 n = if null us then 0 else fst $ head us
where us = filter ((== 1) . snd) $ zip (a027748_row n) (a124010_row n)
(Python)
from sympy import factorint, prime, primepi, isprime, primefactors
def a049084(n): return primepi(n)*(1*isprime(n))
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def a028234(n):
f = factorint(n)
return 1 if n==1 else n/(min(f)**f[min(f)])
def a067029(n):
f=factorint(n)
return 0 if n==1 else f[min(f)]
def a277697(n): return 0 if n==1 else a055396(n) if a067029(n)==1 else a277697(a028234(n))
def a(n): return 0 if a277697(n)==0 else prime(a277697(n)) # Indranil Ghosh, May 16 2017
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CROSSREFS
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Cf. A277698 for a variant which gives 1's instead of 0's for numbers with no unitary prime divisors (A001694).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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