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A247938
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Sum of divisors of 2^prime(n)-1.
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2
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4, 8, 32, 128, 2160, 8192, 131072, 524288, 8567136, 539922240, 2147483648, 138055271872, 2199187780272, 8817412930560, 140828559963840, 9008745449302368, 576463955735383776, 2305843009213693952, 147573953351708377936, 2361193635521975063040
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OFFSET
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1,1
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COMMENTS
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b-file computed with factorizations in Wagstaff link. a(167) corresponding to 2^991-1 is currently the first unknown term. - Jens Kruse Andersen, Sep 28 2014
Conjecture: a(n)/2^prime(n) reaches its maximum value 135/128 at n = 5. - Jianing Song, Dec 31 2022
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REFERENCES
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R. Bojanić, Asymptotic evaluations of the sum of divisors of certain numbers (in Serbo-Croatian), Bull. Soc. Math.-Phys, R.P. Macédoine, Vol. 5 (1954), pp. 5-15.
József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 96.
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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Table[DivisorSigma[1, 2^Prime[n]-1], {n, 30}]
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PROG
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(Magma) [SumOfDivisors(2^p-1): p in PrimesUpTo(100)];
(PARI) vector(50, n, sigma(2^prime(n)-1)) \\ Derek Orr, Sep 27 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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