A347076 Numbers m such that tau(m) = tau(m-1) + tau(m+1) and simultaneously sigma(m) = sigma(m-1) + sigma(m+1).

89484, 167784, 8587065618, 24033737496, 41249560520, 161721015522, 206958258156, 441151731162, 600656241732, 1013494535238, 4648478084262, 5099258875122, 7897343836494, 21060284613738, 26847208137084

Offset: 1

Author

Jaroslav Krizek, Aug 15 2021

Keywords

• nonn
• more

Comments

Intersection of A073500 and A090502.

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

Examples

			tau(89484) = tau(89483) + tau(89485); 12 = 4 + 8.
sigma(89484) = sigma(89483) + sigma(89485); 208824 = 91608 + 117216.
		

Crossrefs

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

Programs

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)]

Mathematica

Select[Range[200000], DivisorSigma[{0, 1}, # - 1] + DivisorSigma[{0, 1}, # + 1] - DivisorSigma[{0, 1}, # ] == {0, 0} &] (* Amiram Eldar, Aug 16 2021 *)

Extensions

a(14)-a(15) from Martin Ehrenstein, Sep 24 2021