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A277885
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a(n) = index of the least non-unitary prime divisor of n or 0 if no such prime-divisor exists.
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3
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0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 3, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 4, 3, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 4, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1
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OFFSET
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1,9
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from prime indices
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FORMULA
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a(1) = 0; for n > 1, if A067029(n) > 1, a(n) = A055396(n), otherwise a(n) = a(A028234(n)). [One may use A032742 instead of A028234 for recursing.]
A008578(1+a(n))) = A249739(n).
For n > 1, a(n) + A277697(n) > 0.
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MATHEMATICA
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Table[PrimePi@ Min[Select[FactorInteger[n][[All, 1]], ! CoprimeQ[#, n/#] &] /. {} -> 0], {n, 120}] (* Michael De Vlieger, Nov 15 2016 *)
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PROG
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(Scheme) (definec (A277885 n) (cond ((= 1 n) 0) ((< 1 (A067029 n)) (A055396 n)) (else (A277885 (A028234 n)))))
(Python)
from sympy import factorint, 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 a(n): return 0 if n==1 else a055396(n) if a067029(n)>1 else a(a028234(n)) # Indranil Ghosh, May 15 2017
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CROSSREFS
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Cf. A008578, A028234, A032742, A055396, A067029, A249739.
Cf. A277697.
Cf. A005117 (gives the positions of zeros).
Sequence in context: A219486 A284574 A206499 * A109527 A186715 A219485
Adjacent sequences: A277882 A277883 A277884 * A277886 A277887 A277888
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Nov 08 2016
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STATUS
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approved
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