A366576
Sum of the divisors of 3^n-1.
Original entry on oeis.org
3, 15, 42, 186, 399, 1680, 3282, 15876, 31836, 123690, 277344, 1541568, 2391486, 8992680, 25483332, 111757968, 193819392, 967814400, 1744488660, 9366647892, 16912999320, 62424587520, 144219337920, 852903426816, 1397135488896, 4766016364260, 12477973754400
Offset: 1
a(4)=186 because 3^4-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.
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a:=n->numtheory[sigma](3^n-1):
seq(a(n), n=1..100);
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DivisorSigma[1,3^Range[30]-1] (* Paolo Xausa, Oct 15 2023 *)
A366718
Largest prime factor of 12^n - 1.
Original entry on oeis.org
11, 13, 157, 29, 22621, 157, 4943, 233, 80749, 22621, 266981089, 20593, 20369233, 13063, 22621, 260753, 74876782031, 80749, 29043636306420266077, 85403261, 8177824843189, 57154490053, 321218438243, 2227777, 12629757106815551, 20369233, 86769286104133
Offset: 1
- Max Alekseyev, Table of n, a(n) for n = 1..310
- J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
Cf.
A024140,
A006530,
A005420,
A074477,
A274906,
A074479,
A274907,
A074249,
A274908,
A274909,
A005422,
A274910,
A366707,
A366708,
A366709,
A366710,
A366711,
A366717,
A366720.
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[Maximum(PrimeDivisors(12^n-1)): n in [1..40]];
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Table[FactorInteger[12^n - 1][[-1, 1]], {n, 40}]