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A334210
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a(n) = sigma(prime(n) + 1) - sigma(prime(n)).
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0
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1, 3, 6, 7, 16, 10, 21, 22, 36, 42, 31, 22, 54, 40, 76, 66, 108, 34, 58, 123, 40, 106, 140, 144, 73, 114, 106, 172, 106, 126, 127, 204, 150, 196, 222, 148, 82, 130, 312, 186, 366, 154, 316, 100, 270, 265, 166, 280, 332, 202, 312, 504, 157, 476, 270, 456, 450, 286, 142, 294
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OFFSET
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1,2
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COMMENTS
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Lim_{n->oo} a(n) = oo because a(n) > sqrt(prime(n)) [see the reference], but this sequence is not monotone increasing.
a(n) is the sum of aliquot parts of the sum of divisors of n-th prime (see Marcus's formula). - Omar E. Pol, Apr 18 2020
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REFERENCES
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J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 617 pp. 82, 280, Ellipses, Paris, 2004.
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LINKS
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FORMULA
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EXAMPLE
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As prime(6) = 13, a(6) = sigma(14) - sigma(13) = 24 - 14 = 10.
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MAPLE
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G:= seq(sigma(ithprime(p)+1)-sigma(ithprime(p)), p=1..200);
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MATHEMATICA
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(DivisorSigma[1, # + 1] - # - 1)& @ Select[Range[300], PrimeQ] (* Amiram Eldar, Apr 18 2020 *)
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PROG
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(PARI) a(n) = my(p=prime(n)); sigma(p+1) - (p+1); \\ Michel Marcus, Apr 18 2020
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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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