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A358760 Numbers k for which A349905(k) is a multiple of 4, where A349905(k) is the arithmetic derivative applied to the prime shifted k.

%I A358760 #16 Nov 30 2023 02:54:25
%S A358760 1,6,15,16,21,22,26,36,40,46,51,55,56,57,62,65,74,77,81,87,90,91,94,
%T A358760 96,100,115,118,123,126,129,132,136,140,142,152,155,156,159,161,166,
%U A358760 178,183,185,187,194,196,201,209,214,216,217,218,219,221,225,232,235,237,240,247,250,256,259,262,276
%N A358760 Numbers k for which A349905(k) is a multiple of 4, where A349905(k) is the arithmetic derivative applied to the prime shifted k.
%C A358760 Numbers k such that A003961(k) is one of the terms of A327864.
%C A358760 Numbers k such that A001222(k) == A003961(k)-1 (modulo 4).
%H A358760 Robert Israel, <a href="/A358760/b358760.txt">Table of n, a(n) for n = 1..10000</a>
%H A358760 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A358760 {k | A010873(A349905(k)) = 0}.
%p A358760 filter:= proc(n) local m,np,F, F1,F2, i;
%p A358760   F:= ifactors(n)[2];
%p A358760   m:= nops(F);
%p A358760   F1:= map(nextprime, F[..,1]);
%p A358760   F2:= F[..,2];
%p A358760   np:= mul(F1[i]^F2[i],i=1..m);
%p A358760   np*add(F2[i]/F1[i],i=1..m) mod 4 = 0;
%p A358760 end proc:
%p A358760 select(filter, [$1..1000]); # _Robert Israel_, Nov 29 2023
%o A358760 (PARI) isA358760(n) = A358750(n);
%Y A358760 Cf. A001222, A003415, A003961, A010873, A121262, A246260, A327864, A349905, A358750 (characteristic function).
%Y A358760 Setwise difference A028260 \ A358762.
%Y A358760 Cf. also A358761, A358763.
%K A358760 nonn
%O A358760 1,2
%A A358760 _Antti Karttunen_, Nov 29 2022