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A034714 Dirichlet convolution of squares with themselves. 6
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

Erich Friedman

STATUS

approved

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Last modified February 25 14:40 EST 2021. Contains 341609 sequences. (Running on oeis4.)