cp's OEIS Frontend

A174568 Numbers n such that phi(n) + sigma(n) = sigma(n + phi(n)).

%I A174568 #21 Jun 02 2025 02:44:16
%S A174568 2,3,7,19,31,37,79,97,99,135,139,157,198,199,211,229,271,287,307,331,
%T A174568 337,350,367,379,439,499,539,547,577,601,607,619,661,671,691,727,811,
%U A174568 829,877,923,937,967,997,1009,1069,1171,1237,1254,1279,1297,1399,1429
%N A174568 Numbers n such that phi(n) + sigma(n) = sigma(n + phi(n)).
%C A174568 A005382 is included in this sequence : if p and 2p-1 primes, phi(p) = p-1, sigma(p)=p+1 and sigma(2p-1)=2p => phi(p) +sigma(p) = sigma(p+phi(p)). See the similar sequence A005384.
%D A174568 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
%H A174568 Amiram Eldar, <a href="/A174568/b174568.txt">Table of n, a(n) for n = 1..10000</a>
%H A174568 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%e A174568 2 is in the sequence because phi(2) + sigma(2) = 1 + 3 = 4, and sigma(2 + phi(2)) = sigma(3) = 4;
%e A174568 99 is in the sequence because phi(99) + sigma(99) = 60 + 156 = 216, and sigma(99 + phi(99)) = sigma(159) = 216.
%p A174568 with(numtheory):for n from 1 to 3000 do :if phi(n)+sigma(n) = sigma(n+phi(n)) then print(n):else fi:od:
%t A174568 Select[Range[1500],EulerPhi[#]+DivisorSigma[1,#]==DivisorSigma[1, #+ EulerPhi[ #]]&] (* _Harvey P. Dale_, Jul 05 2018 *)
%o A174568 (Magma) [n: n in [1..1500] | (EulerPhi(n) + SumOfDivisors(n)) eq (SumOfDivisors(n + EulerPhi(n)))]; // _Vincenzo Librandi_, Jul 15 2015
%Y A174568 Cf. A005382, A005384, A057326, A057327, A057328, A057330, A005603.
%K A174568 nonn
%O A174568 1,1
%A A174568 _Michel Lagneau_, Mar 22 2010