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 A034714 Dirichlet convolution of squares with themselves. 8
 1, 8, 18, 48, 50, 144, 98, 256, 243, 400, 242, 864, 338, 784, 900, 1280, 578, 1944, 722, 2400, 1764, 1936, 1058, 4608, 1875, 2704, 2916, 4704, 1682, 7200, 1922, 6144, 4356, 4624, 4900, 11664, 2738, 5776, 6084, 12800, 3362, 14112, 3698, 11616, 12150, 8464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Bruno Berselli, Table of n, a(n) for n = 1..1000 Joerg Arndt, On computing the generalized Lambert series, arXiv:1202.6525v3 [math.CA], (2012). FORMULA Dirichlet g.f.: zeta^2(x-2). Equals n^2*tau(n), where tau(n) = A000005(n) = number of divisors of n. - Jon Perry, Aug 28 2005 Multiplicative with a(p^e) = (e+1)p^(2e). - Mitch Harris, Jun 27 2005 Row sums of triangle A134576. - Gary W. Adamson, Nov 02 2007 G.f.: Sum_{k>=1} k^2*x^k*(1 + x^k)/(1 - x^k)^3. - Ilya Gutkovskiy, Oct 24 2018 a(n) = n * A038040(n). - Torlach Rush, Feb 01 2019 Sum_{k>=1} 1/a(k) = Product_{primes p} (-p^2 * log(1 - 1/p^2)) = 1.27728092754165872535305748273941301416624226497497308879403022758421224... - Vaclav Kotesovec, Sep 19 2020 G.f.: Sum_{n >= 1} q^(n^2)*( n^4*q^(3*n) - n^2*(n^2 + 4*n - 2)*q^(2*n) - n^2*(n^2 - 4*n - 2)*q^n + n^4 )/(1 - q^n)^3 - apply the operator q*d/dq twice to equation 5 in Arndt and set x = 1. - Peter Bala, Jan 21 2021 MAPLE A034714 := proc(n) n^2*numtheory[tau](n) ; end proc: seq(A034714(n), n=1..20) ; # R. J. Mathar, Feb 03 2011 MATHEMATICA A034714[n_]:=DivisorSigma[0, n]*n^2; Array[A034714, 50] (* Enrique Pérez Herrero, Jun 26 2011 *) PROG (PARI) A034714(n)=numdiv(n)*n^2 \\ Enrique Pérez Herrero, Jun 26 2011 (Magma) [n^2*NumberOfDivisors(n): n in [1..50]]; // Bruno Berselli, Feb 12 2014 CROSSREFS Cf. A038040, A134576, A319085. Sequence in context: A279899 A192311 A300161 * A153388 A109988 A335440 Adjacent sequences: A034711 A034712 A034713 * A034715 A034716 A034717 KEYWORD nonn,mult AUTHOR STATUS approved

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Last modified March 22 08:17 EDT 2023. Contains 361419 sequences. (Running on oeis4.)