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A354515 Numbers k such that m - gpf(m) = k has no solution m >= 2, gpf = A006530.

%I A354515 #18 Aug 17 2022 05:07:05
%S A354515 1,4,8,12,16,18,27,32,36,48,50,54,60,64,72,80,81,84,90,96,100,108,112,
%T A354515 125,128,132,135,144,147,150,160,162,176,180,192,196,198,200,208,210,
%U A354515 216,224,225,234,242,243,250,252,256,270,275,280,288,294,300,306,320,324
%N A354515 Numbers k such that m - gpf(m) = k has no solution m >= 2, gpf = A006530.
%C A354515 Numbers k such that there is no prime p such that gpf(k+p) = p.
%C A354515 Numbers k such that there is no prime factor p of k such that k+p is p-smooth.
%H A354515 Jianing Song, <a href="/A354515/b354515.txt">Table of n, a(n) for n = 1..9826</a> (all terms <= 80000)
%e A354515 12 is a term since the prime factors of 12 are 2,3, and we have gpf(12+2) != 2 and gpf(12+3) != 3.
%o A354515 (PARI) gpf(n) = vecmax(factor(n)[, 1]);
%o A354515 isA354515(n) = if(n, my(f=factor(n)[, 1]); for(i=1, #f, if(gpf(n+f[i])==f[i], return(0))); 1, 0)
%Y A354515 Cf. A006530, A076563.
%Y A354515 Indices of 0 in A354512. Complement of A354514.
%K A354515 nonn,easy
%O A354515 1,2
%A A354515 _Jianing Song_, Aug 16 2022