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A321295
a(n) = n * sigma_n(n).
1
1, 10, 84, 1092, 15630, 284700, 5764808, 134744072, 3486961557, 100097666500, 3138428376732, 107019534520152, 3937376385699302, 155577590681061500, 6568408813691796120, 295152408847700721680, 14063084452067724991026, 708238048886859220660710
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>=1} k^(k+1)*x^k/(1 - (k*x)^k)^2.
a(n) = Sum_{d|n} phi(n/d)*sigma_(n+1)(d).
a(n) = n * A023887(n).
MATHEMATICA
Table[n DivisorSigma[n, n], {n, 18}]
nmax = 18; Rest[CoefficientList[Series[Sum[k^(k + 1) x^k/(1 - (k x)^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]]
Table[Sum[EulerPhi[n/d] DivisorSigma[n + 1, d], {d, Divisors[n]}], {n, 18}]
PROG
(PARI) a(n) = n*sigma(n, n); \\ Michel Marcus, Nov 03 2018
(Perl) use ntheory ":all"; say "$_ ", vecprod($_, divisor_sum($_, $_)) for 1..30; # Dana Jacobsen, Nov 05 2018
(Magma) [n*DivisorSigma(n, n): n in [1..20]]; // Vincenzo Librandi, Nov 06, 2018
CROSSREFS
Sequence in context: A364416 A155593 A239990 * A350903 A318793 A104128
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 02 2018
STATUS
approved