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A259673
a(n) = sigma_(prime(n))(n).
2
1, 9, 244, 16513, 48828126, 13062296532, 232630513987208, 144115462954287105, 8862938119746644274757, 100000000186264514923632574038, 191943424957750480504146841291812, 8505622499882988712256991112913772434548, 4695452425098908797088971409337422035076128814
OFFSET
1,2
FORMULA
a(n) = sigma_(A000040(n))(n).
a(n) = [x^n] Sum_{k>=1} k^prime(n)*x^k/(1 - x^k). - Ilya Gutkovskiy, Sep 26 2017
MAPLE
a:= n-> numtheory[sigma][ithprime(n)](n):
seq(a(n), n=1..15); # Alois P. Heinz, Feb 10 2020
MATHEMATICA
a[n_] := DivisorSigma[Prime[n], n]; Array[a, 13]
(* Second program: *)
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 *)
PROG
(PARI) a(n) = sigma(n, prime(n)); \\ Michel Marcus, Jul 03 2015
(Magma) [DivisorSigma(NthPrime(n), n):n in [1..15]]; // Vincenzo Librandi, Jul 15 2015
(Python)
from sympy import divisor_sigma, prime
def A259673(n):
....return divisor_sigma(n, prime(n)) # Chai Wah Wu, Jul 20 2015
CROSSREFS
Cf. A000203 (sigma(n)), A000040 (prime(n)), A023887 (sigma_n(n)).
Cf. A001157 (sigma_2), A001158 (sigma_3), A001160 (sigma_5), A013955 (sigma_7).
Sequence in context: A329305 A183235 A359732 * A272234 A272240 A161159
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Jul 03 2015
EXTENSIONS
a(11) and a(12) from Anders Hellström, Jul 14 2015
STATUS
approved