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%I #40 Apr 26 2020 05:27:32
%S 1,3,6,7,16,10,21,22,36,42,31,22,54,40,76,66,108,34,58,123,40,106,140,
%T 144,73,114,106,172,106,126,127,204,150,196,222,148,82,130,312,186,
%U 366,154,316,100,270,265,166,280,332,202,312,504,157,476,270,456,450,286,142,294
%N a(n) = sigma(prime(n) + 1) - sigma(prime(n)).
%C Lim_{n->oo} a(n) = oo because a(n) > sqrt(prime(n)) [see the reference], but this sequence is not monotone increasing.
%C 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
%D J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 617 pp. 82, 280, Ellipses, Paris, 2004.
%F a(n) = A008333(n) - A008864(n).
%F From _Michel Marcus_, Apr 18 2020: (Start)
%F a(n) = A001065(A008864(n)).
%F a(n) = A051027(prime(n)) - A000203(prime(n)). (End)
%e As prime(6) = 13, a(6) = sigma(14) - sigma(13) = 24 - 14 = 10.
%p G:= seq(sigma(ithprime(p)+1)-sigma(ithprime(p)), p=1..200);
%t (DivisorSigma[1, # + 1] - # - 1)& @ Select[Range[300], PrimeQ] (* _Amiram Eldar_, Apr 18 2020 *)
%o (PARI) a(n) = my(p=prime(n)); sigma(p+1) - (p+1); \\ _Michel Marcus_, Apr 18 2020
%Y Cf. A000203, A001065, A008333, A008864, A051027.
%K nonn
%O 1,2
%A _Bernard Schott_, Apr 18 2020
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