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Positive integers that cannot be written in the form k - gpf(k) +- 1 for some integer k, where gpf(k) is the greatest prime factor of k.
1

%I #15 Apr 12 2021 21:45:37

%S 17,49,161,197,199,209,251,391,419,449,649,685,769,799,883,967,1057,

%T 1189,1249,1301,1457,1481,1681,1793,1937,1979,2001,2029,2089,2177,

%U 2209,2311,2377,2379,2419,2431,2449,2549,2551,2575,2591,2705,2729,2899,3041,3073

%N Positive integers that cannot be written in the form k - gpf(k) +- 1 for some integer k, where gpf(k) is the greatest prime factor of k.

%H Robert Israel, <a href="/A342609/b342609.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local g;

%p g:= max(numtheory:-factorset(n));

%p n-g+1,n-g-1

%p end proc:

%p sort(convert({$1..5000} minus map(f, {$1..10001}),list)); # _Robert Israel_, Apr 12 2021

%Y Cf. A006530, A076563.

%K nonn

%O 1,1

%A _Christian Bagshaw_, Mar 16 2021