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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..385

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

Cf. A023887, A064987.

Sequence in context: A335647 A155593 A239990 * A318793 A104128 A014341

Adjacent sequences:  A321292 A321293 A321294 * A321296 A321297 A321298

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 02 2018

STATUS

approved

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Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)