id:A069733 - OEIS Search Results

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Number of divisors m of n such that m or n/m is odd. Number of non-orientable coverings of the Klein bottle with n lists.

+0
5

1, 2, 2, 2, 2, 4, 2, 2, 3, 4, 2, 4, 2, 4, 4, 2, 2, 6, 2, 4, 4, 4, 2, 4, 3, 4, 4, 4, 2, 8, 2, 2, 4, 4, 4, 6, 2, 4, 4, 4, 2, 8, 2, 4, 6, 4, 2, 4, 3, 6, 4, 4, 2, 8, 4, 4, 4, 4, 2, 8, 2, 4, 6, 2, 4, 8, 2, 4, 4, 8, 2, 6, 2, 4, 6, 4, 4, 8, 2, 4, 5, 4, 2, 8, 4, 4, 4, 4, 2, 12, 4, 4, 4, 4, 4, 4, 2, 6, 6, 6, 2, 8, 2, 4 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`Multiplicative defined by f(2^k)=2 and f(p^k)=k+1 for k>0 and an odd prime p.` `Also number of divisors of n that are not divisible by 4. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 16 2002`
	LINKS	`V. A. Liskovets and A. Mednykh, Number of non-orientable coverings of the Klein bottle`
	FORMULA	`a(n) == d(n)-d(n/4) for 4\|n and =d(n) otherwise where d(n) is the number of divisors of n (A000005).` `G.f.: Sum_{m>0} x^m(1+x^m+x^(2m))/(1-x^(4*m)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 21 2002`
	PROGRAM	`(PARI) a(n)=if(n<1, 0, sumdiv(n, d, sign(d%4)))`
	CROSSREFS	`Cf. A069184.` `Cf. A046897.` `Sequence in context: A073180 A127973 A023157 this_sequence A081755 A097859 A028326` `Adjacent sequences: A069730 A069731 A069732 this_sequence A069734 A069735 A069736`
	KEYWORD	`mult,easy,nonn`
	AUTHOR	`Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002`

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Last modified December 8 08:31 EST 2009. Contains 170430 sequences.

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