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A038991 Number of sublattices of index n in generic 4-dimensional lattice. 4
1, 15, 40, 155, 156, 600, 400, 1395, 1210, 2340, 1464, 6200, 2380, 6000, 6240, 11811, 5220, 18150, 7240, 24180, 16000, 21960, 12720, 55800, 20306, 35700, 33880, 62000, 25260, 93600, 30784, 97155, 58560, 78300, 62400, 187550, 52060, 108600, 95200, 217620, 70644, 240000, 81400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

M. Baake and U. Grimm, Combinatorial problems of (quasi)crystallography, arXiv:math-ph/0212015, 2002.

M. Baake, N. Neumarker, A Note on the Relation Between Fixed Point and Orbit Count Sequences, JIS 12 (2009) 09.4.4, Section 3.

Tad White, Counting Free Abelian Actions, arXiv preprint arXiv:1304.2830 [math.CO], 2013.

Index entries for sequences related to sublattices

FORMULA

f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=4.

Dirichlet g.f.: zeta(s)*zeta(s-1)*zeta(s-2)*zeta(s-3).

Dirichlet convolution of A000578 and A001001.

Multiplicative with a(p^e) = Product_{k=1..3} (p^(e+k)-1)/(p^k-1).

Sum_{k=1..n} a(k) ~ Pi^6 * Zeta(3) * n^4 / 2160. - Vaclav Kotesovec, Feb 01 2019

MATHEMATICA

a[n_] := DivisorSum[n, #*DivisorSum[#, #*DivisorSum[#, #&]&]&]; Array[a, 50] (* Jean-Fran├žois Alcover, Dec 02 2015, after Joerg Arndt *)

PROG

(PARI) a(n)=sumdiv(n, x, x * sumdiv(x, y, y * sumdiv(y, z, z ) ) ); /* Joerg Arndt, Oct 07 2012 */

CROSSREFS

Cf. A001001.

Sequence in context: A160891 A223425 A175926 * A068020 A131991 A116042

Adjacent sequences:  A038988 A038989 A038990 * A038992 A038993 A038994

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed from 0 to 1 by R. J. Mathar, Mar 31 2011

More terms from Joerg Arndt, Oct 07 2012

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)