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A259673 a(n) = sigma_(prime(n))(n).

%I A259673 #45 May 22 2025 10:21:43
%S A259673 1,9,244,16513,48828126,13062296532,232630513987208,
%T A259673 144115462954287105,8862938119746644274757,
%U A259673 100000000186264514923632574038,191943424957750480504146841291812,8505622499882988712256991112913772434548,4695452425098908797088971409337422035076128814
%N A259673 a(n) = sigma_(prime(n))(n).
%H A259673 Anders Hellström, <a href="/A259673/b259673.txt">Table of n, a(n) for n = 1..50</a>
%H A259673 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A259673 a(n) = sigma_(A000040(n))(n).
%F A259673 a(n) = [x^n] Sum_{k>=1} k^prime(n)*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Sep 26 2017
%p A259673 a:= n-> numtheory[sigma][ithprime(n)](n):
%p A259673 seq(a(n), n=1..15);  # _Alois P. Heinz_, Feb 10 2020
%t A259673 a[n_] := DivisorSigma[Prime[n], n]; Array[a, 13]
%t A259673 (* Second program: *)
%t A259673 a[n_] := SeriesCoefficient[Sum[k^Prime[n]*x^k/(1-x^k), {k, 1, n}], {x, 0, n}]; Array[a, 13] (* _Jean-François Alcover_, Sep 29 2017, from 2nd formula *)
%o A259673 (PARI) a(n) = sigma(n, prime(n)); \\ _Michel Marcus_, Jul 03 2015
%o A259673 (Magma) [DivisorSigma(NthPrime(n),n):n in [1..15]]; // _Vincenzo Librandi_, Jul 15 2015
%o A259673 (Python)
%o A259673 from sympy import divisor_sigma, prime
%o A259673 def A259673(n):
%o A259673     return divisor_sigma(n,prime(n)) # _Chai Wah Wu_, Jul 20 2015
%Y A259673 Cf. A000203 (sigma(n)), A000040 (prime(n)), A023887 (sigma_n(n)).
%Y A259673 Cf. A001157 (sigma_2), A001158 (sigma_3), A001160 (sigma_5), A013955 (sigma_7).
%K A259673 nonn,easy
%O A259673 1,2
%A A259673 _Ilya Gutkovskiy_, Jul 03 2015
%E A259673 a(11) and a(12) from _Anders Hellström_, Jul 14 2015