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A061853 Difference between smallest prime not dividing n and smallest nondivisor of n.

%I A061853 #26 Apr 21 2021 11:25:44
%S A061853 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,
%T A061853 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,
%U A061853 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
%N A061853 Difference between smallest prime not dividing n and smallest nondivisor of n.
%C A061853 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).
%C A061853 Primorials from A002110(2)=6 onward seem to give the positions of records. - _Antti Karttunen_, Jul 28 2017
%C A061853 Difference between the smallest prime coprime to n and the smallest non-divisor of n. - _Michael De Vlieger_, Jul 28 2017
%H A061853 Antti Karttunen, <a href="/A061853/b061853.txt">Table of n, a(n) for n = 1..30030</a>
%F A061853 a(n) = A053669(n) - A007978(n).
%e A061853 a(29)=2-2=0; a(30)=7-4=3; a(420)=11-8=3.
%o A061853 (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
%o A061853 (Python)
%o A061853 from sympy import nextprime
%o A061853 def a053669(n):
%o A061853     p=2
%o A061853     while n%p==0: p=nextprime(p)
%o A061853     return p
%o A061853 def a007978(n):
%o A061853     p=2
%o A061853     while n%p==0: p+=1
%o A061853     return p
%o A061853 def a(n): return a053669(n) - a007978(n)
%o A061853 print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jul 29 2017
%Y A061853 Cf. A002110, A007978, A053669.
%K A061853 nonn
%O A061853 1,30
%A A061853 _Henry Bottomley_, May 10 2001
%E A061853 Description corrected by _Michael De Vlieger_, Jul 28 2017