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A061853
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Difference between smallest prime not dividing n and smallest nondivisor of n.
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2
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0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
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OFFSET
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1,30
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COMMENTS
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a(12m+6) is always positive since it involves subtracting 4 from a larger number; the first case where a term not of this form is positive is a(420).
Difference between the smallest prime coprime to n and the smallest non-divisor of n. - Michael De Vlieger, Jul 28 2017
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LINKS
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FORMULA
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EXAMPLE
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a(29)=2-2=0; a(30)=7-4=3; a(420)=11-8=3.
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PROG
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(PARI) a(n) = {my(f = factor(n), d = divisors(f), res, p = 2, i = 1, j); while(i<=#f~ && f[i, 1]==p, i++; p = nextprime(p+1)); res = p; for(j=2, #d, if(d[j]!=j, return(res - d[j-1] - 1)))} \\ David A. Corneth, Jul 29 2017
(Python)
from sympy import nextprime
def a053669(n):
p=2
while n%p==0: p=nextprime(p)
return p
def a007978(n):
p=2
while n%p==0: p+=1
return p
def a(n): return a053669(n) - a007978(n)
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CROSSREFS
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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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