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A347076
Numbers m such that tau(m) = tau(m-1) + tau(m+1) and simultaneously sigma(m) = sigma(m-1) + sigma(m+1).
1
89484, 167784, 8587065618, 24033737496, 41249560520, 161721015522, 206958258156, 441151731162, 600656241732, 1013494535238, 4648478084262, 5099258875122, 7897343836494, 21060284613738, 26847208137084
OFFSET
1,1
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
EXAMPLE
tau(89484) = tau(89483) + tau(89485); 12 = 4 + 8.
sigma(89484) = sigma(89483) + sigma(89485); 208824 = 91608 + 117216.
MATHEMATICA
Select[Range[200000], DivisorSigma[{0, 1}, # - 1] + DivisorSigma[{0, 1}, # + 1] - DivisorSigma[{0, 1}, # ] == {0, 0} &] (* Amiram Eldar, Aug 16 2021 *)
PROG
(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)]
CROSSREFS
Cf. A000005 (tau), A000203 (sigma), A073500, A090502.
Sequence in context: A184028 A209896 A255390 * A205290 A205898 A250452
KEYWORD
nonn,more
AUTHOR
Jaroslav Krizek, Aug 15 2021
EXTENSIONS
a(14)-a(15) from Martin Ehrenstein, Sep 24 2021
STATUS
approved