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A307414 Numbers k such that A014285(k) and A007504(k) are coprime.

%I A307414 #18 Dec 05 2023 08:25:08
%S A307414 2,3,6,7,10,11,12,14,15,18,19,22,23,24,27,30,31,32,34,35,38,39,40,44,
%T A307414 46,47,48,51,52,55,56,58,59,60,63,64,66,67,70,71,72,74,75,76,78,79,82,
%U A307414 83,86,87,88,91,92,94,95,96,98,99,100,102,104,106,108,110,112,114,115,116,118,119,120,122
%N A307414 Numbers k such that A014285(k) and A007504(k) are coprime.
%C A307414 Numbers k such that A306834(k) = A014285(k).
%C A307414 No terms == 1 (mod 4).
%C A307414 Numbers k such that A309036(k)=1. - _Robert Israel_, Jul 09 2019
%H A307414 Robert Israel, <a href="/A307414/b307414.txt">Table of n, a(n) for n = 1..10000</a>
%e A307414 a(3) = 6 is a term because A007504(6) = 41 and A014285(6) = 184 are coprime.
%p A307414 N:= 1000: # for terms <= N
%p A307414 Primes:= map(ithprime, [$1..N]):
%p A307414 S1:= ListTools:-PartialSums(Primes):
%p A307414 S2:= ListTools:-PartialSums(zip(`*`,Primes, [$1..N])):
%p A307414 select(t -> igcd(S1[t],S2[t])=1, [$1..N]);
%t A307414 okQ[n_] := With[{pp = Prime[Range[n]]}, CoprimeQ[Total[pp], Total[pp.Range[n]]]];
%t A307414 Select[Range[200], okQ] (* _Jean-François Alcover_, Dec 05 2023 *)
%o A307414 (PARI) isok(k) = my(vp=primes(k)); gcd(sum(i=1, k, vp[i]), sum(i=1, k, i*vp[i])) == 1; \\ _Michel Marcus_, Apr 07 2019
%Y A307414 Cf. A007504, A014285, A306834, A309036.
%K A307414 nonn
%O A307414 1,1
%A A307414 _Robert Israel_, Apr 07 2019