cp's OEIS Frontend

A164114 Numbers k such that Chowla(k) + phi(k) is prime.

%I A164114 #19 Sep 08 2022 08:45:47
%S A164114 3,6,10,12,20,22,24,44,46,54,58,66,68,70,78,80,82,84,88,90,106,116,
%T A164114 120,136,138,154,156,160,166,168,174,178,184,186,188,190,192,212,226,
%U A164114 234,246,250,252,258,262,270,284,286,300,306,318,320,328,330,332,336,346,352,356
%N A164114 Numbers k such that Chowla(k) + phi(k) is prime.
%C A164114 Indices such that the sum of the nontrivial divisors and of the Euler totient function at that index is prime.
%H A164114 G. C. Greubel, <a href="/A164114/b164114.txt">Table of n, a(n) for n = 1..5000</a>
%F A164114 {k: A048050(k)+A000010(k) in A000040}.
%e A164114 n=3 is in the sequence because Chowla(3) + phi(3) = 0 + 2 = 2 (a prime);
%e A164114 n=6 is in the sequence because Chowla(6) + phi(5) = 5 + 2 = 7 (a prime).
%p A164114 A048050 := proc(n) if n = 1 then 0; else numtheory[sigma](n)-n-1 ; fi; end:
%p A164114 A000010 := proc(n) numtheory[phi](n) ; end: isA164114 := proc(n) isprime( A000010(n)+A048050(n)) ; end:
%p A164114 for n from 1 to 400 do if isA164114(n) then printf("%d,",n): fi; od: # _R. J. Mathar_, Aug 27 2009
%t A164114 f[n_] := Plus @@ Divisors[n] - n - 1; Select[Range[100], PrimeQ[f[#] + EulerPhi[#]] &] (* _G. C. Greubel_, Sep 11 2017 *)
%o A164114 (PARI) isok(n) = isprime(sigma(n)+eulerphi(n)-n-1); \\ _Michel Marcus_, Sep 12 2017
%o A164114 (Magma) [n: n in [1..400] | IsPrime((SumOfDivisors(n)+EulerPhi(n))-n-1)]; // _Vincenzo Librandi_, Sep 12 2017
%Y A164114 Cf. A000010, A000040, A000203, A048050.
%K A164114 nonn
%O A164114 1,1
%A A164114 _Juri-Stepan Gerasimov_, Aug 10 2009
%E A164114 34 and 60 removed, 54 inserted by _R. J. Mathar_, Aug 27 2009