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A259496 Numbers n such that phi(n) + d(n) = phi(n+1) + d(n+1), where phi(n) is the Euler totient function of n and d(n) the number of divisors of n.

%I A259496 #39 Sep 08 2022 08:46:13
%S A259496 5,7,104,105,1754,3255,16215,22935,67431,93074,983775,1025504,2200694,
%T A259496 2619705,3365438,4163355,4447064,4695704,6372794,7838265,9718904,
%U A259496 11903775,23992215,26879684,29357475,37239735,40588485,41207144,48615735,56424555,76466985,81591194,83864055
%N A259496 Numbers n such that phi(n) + d(n) = phi(n+1) + d(n+1), where phi(n) is the Euler totient function of n and d(n) the number of divisors of n.
%C A259496 So far, less than 10^9, except for 7, 67431 &  3365438, all terms have been congruent to 5 or 4 (mod 10). - _Robert G. Wilson v_, Jul 06 2015
%H A259496 Giovanni Resta, <a href="/A259496/b259496.txt">Table of n, a(n) for n = 1..600</a> (first 65 terms from Robert G. Wilson v)
%e A259496 phi(5) + d(5) = 4 + 2 = 6 and phi(6) + d(6) = 2 + 4 = 6.
%e A259496 phi(7) + d(7) = 6 + 2 = 8 and phi(8) + d(8) = 4 + 4 = 8.
%p A259496 with(numtheory): P:=proc(q) local n; for n from 1 to q do
%p A259496 if phi(n)+tau(n)=phi(n+1)+tau(n+1) then print(n); fi;
%p A259496 od; end: P(10^9);
%t A259496 a = k = 2; lst = {}; While[k < 100000001, b = EulerPhi[k] + DivisorSigma[0, k]; If[a == b, AppendTo[lst, k - 1]]; k++; a = b]; lst
%o A259496 (Magma) [n: n in [1..6*10^6] | EulerPhi(n) + NumberOfDivisors(n) eq EulerPhi(n+1) + NumberOfDivisors(n+1)]; // _Vincenzo Librandi_, Jun 30 2015
%Y A259496 Cf. A000005, A000010, A061468, A054004, A145749, A259495.
%K A259496 nonn
%O A259496 1,1
%A A259496 _Paolo P. Lava_, Jun 29 2015
%E A259496 a(23)-a(33) from _Robert G. Wilson v_, Jul 05 2015