cp's OEIS Frontend

A360757 Numbers k for which the arithmetic derivative of k is a Sophie Germain prime (A005384).

%I A360757 #22 May 23 2023 08:16:14
%S A360757 6,42,154,182,222,231,286,357,434,442,455,483,582,595,645,690,742,762,
%T A360757 770,806,861,906,969,987,994,1045,1066,1086,1122,1162,1463,1534,1547,
%U A360757 1554,1582,1738,1742,1771,1798,1869,1905,2065,2121,2193,2265,2274,2282,2365
%N A360757 Numbers k for which the arithmetic derivative of k is a Sophie Germain prime (A005384).
%H A360757 Robert Israel, <a href="/A360757/b360757.txt">Table of n, a(n) for n = 1..10000</a>
%e A360757 6' = 5 is prime and 2*6' + 1 = 2*5 + 1 = 11 is prime, so 6 is a term.
%e A360757 42' = 41 is prime and 2*42' + 1 = 2*41 + 1 = 83 is prime, so 42 is a term.
%p A360757 filter:= proc(n) local np,t;
%p A360757   np:= n*add(t[2]/t[1], t = ifactors(n)[2]);
%p A360757   isprime(np) and isprime(2*np+1)
%p A360757 end proc:
%p A360757 select(filter, [$1..3000]); # _Robert Israel_, Mar 18 2023
%t A360757 d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[2400], PrimeQ[d1 = d[#]] && PrimeQ[2*d1 + 1] &] (* _Amiram Eldar_, Mar 01 2023 *)
%o A360757 (Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [p:p in [1..2500]| IsPrime(Floor(f(p))) and IsPrime(2*Floor(f(p))+1) ];
%Y A360757 Cf. A003415, A005384.
%Y A360757 Subsequence of A157037.
%K A360757 nonn
%O A360757 1,1
%A A360757 _Marius A. Burtea_, Mar 01 2023