A208133 - OEIS

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A208133

Total number of subgroups of rank <=2 of a certain class of abelian groups of order n defined as direct products of Z/(mZ) X Z/(kZ) with m|k.

1, 2, 2, 8, 2, 4, 2, 12, 9, 4, 2, 16, 2, 4, 4, 31, 2, 18, 2, 16, 4, 4, 2, 24, 11, 4, 14, 16, 2, 8, 2, 42, 4, 4, 4, 72, 2, 4, 4, 24, 2, 8, 2, 16, 18, 4, 2, 62, 13, 22, 4, 16, 2, 28, 4, 24, 4, 4, 2, 32, 2, 4, 18, 90, 4, 8, 2, 16, 4, 8, 2, 108, 2, 4, 22, 16 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Level function l_tau^2(n) of Bhowmik and Wu.`
	LINKS	`Table of n, a(n) for n=1..76.` `G. Bhowmik, Jie Wu, Zeta function of subgroups of abelian groups and average orders, J. reine angew. Math. 530 (2001) 1-15`
	FORMULA	`Dirichlet g.f. zeta(s)^2zeta(2s)^2zeta(2s-1)*product_{primes p} [1+1/p^(2s)-2/p^(3s)]`
	MAPLE	`L1 := [ 1, 0, 0, 1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0` `] ;` `L010052 := [ 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ];` `L037213 := [ 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ;` `Lx := DIRICHLET(L1, L037213) ;` `Lx := DIRICHLET(Lx, L010052) ;` `Lx := DIRICHLET(Lx, L010052) ;` `Lx := MOBIUSi(Lx) ;` `Lx := MOBIUSi(Lx) ;`
	CROSSREFS	`Sequence in context: A102645 A037300 A029623 * A046644 A161915 A174354` `Adjacent sequences: A208130 A208131 A208132 * A208134 A208135 A208136`
	KEYWORD	`nonn,mult`
	AUTHOR	`R. J. Mathar, Mar 29 2012`
	STATUS	`approved`

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Last modified May 23 09:48 EDT 2013. Contains 225586 sequences.