%I #20 Sep 08 2022 08:46:26

%S 89484,167784,8587065618,24033737496,41249560520,161721015522,

%T 206958258156,441151731162,600656241732,1013494535238,4648478084262,

%U 5099258875122,7897343836494,21060284613738,26847208137084

%N Numbers m such that tau(m) = tau(m-1) + tau(m+1) and simultaneously sigma(m) = sigma(m-1) + sigma(m+1).

%C Intersection of A073500 and A090502.

%C a(n) is even. If a(n) is odd then two consecutive numbers are perfect squares. This only happens with (0, 1) which does not give terms. - _David A. Corneth_, Aug 16 2021

%e tau(89484) = tau(89483) + tau(89485); 12 = 4 + 8.

%e sigma(89484) = sigma(89483) + sigma(89485); 208824 = 91608 + 117216.

%t Select[Range[200000], DivisorSigma[{0, 1}, # - 1] + DivisorSigma[{0, 1}, # + 1] - DivisorSigma[{0, 1}, # ] == {0, 0} &] (* _Amiram Eldar_, Aug 16 2021 *)

%o (Magma) [m: m in [2..10^5] | #Divisors(m) eq #Divisors(m - 1) + #Divisors(m + 1) and &+Divisors(m) eq &+Divisors(m - 1) + &+Divisors(m + 1)]

%Y Cf. A000005 (tau), A000203 (sigma), A073500, A090502.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Aug 15 2021

%E a(14)-a(15) from _Martin Ehrenstein_, Sep 24 2021