A358760 - OEIS

%I #16 Nov 30 2023 02:54:25

%S 1,6,15,16,21,22,26,36,40,46,51,55,56,57,62,65,74,77,81,87,90,91,94,

%T 96,100,115,118,123,126,129,132,136,140,142,152,155,156,159,161,166,

%U 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 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 Numbers k such that A003961(k) is one of the terms of A327864.

%C Numbers k such that A001222(k) == A003961(k)-1 (modulo 4).

%H Robert Israel, <a href="/A358760/b358760.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F {k | A010873(A349905(k)) = 0}.

%p filter:= proc(n) local m,np,F, F1,F2, i;

%p   F:= ifactors(n)[2];

%p   m:= nops(F);

%p   F1:= map(nextprime, F[..,1]);

%p   F2:= F[..,2];

%p   np:= mul(F1[i]^F2[i],i=1..m);

%p   np*add(F2[i]/F1[i],i=1..m) mod 4 = 0;

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Nov 29 2023

%o (PARI) isA358760(n) = A358750(n);

%Y Cf. A001222, A003415, A003961, A010873, A121262, A246260, A327864, A349905, A358750 (characteristic function).

%Y Setwise difference A028260 \ A358762.

%Y Cf. also A358761, A358763.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 29 2022