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A069733 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. 7
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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, Dec 16 2002

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

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^(2*m))/(1-x^(4*m)). - Vladeta Jovovic, Oct 21 2002

MATHEMATICA

Table[Count[Divisors[n], _?(Mod[#, 4]!=0&)], {n, 110}] (* Harvey P. Dale, Jan 10 2016 *)

PROG

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, sign(d%4)))

(Scheme, with memoization-macro definec) (definec (A069733 n) (cond ((= 1 n) n) ((even? n) (* 2 (A069733 (A000265 n)))) (else (* (+ 1 (A067029 n)) (A069733 (A028234 n)))))) ;; Antti Karttunen, Sep 23 2017

CROSSREFS

Cf. A046897, A069184.

Sequence in context: A300654 A023157 A228849 * A187467 A081755 A237709

Adjacent sequences:  A069730 A069731 A069732 * A069734 A069735 A069736

KEYWORD

mult,easy,nonn

AUTHOR

Valery A. Liskovets, Apr 07 2002

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)