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 A069733 Number of divisors d of n such that d or n/d 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 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 Valery A. Liskovets and Alexander Mednykh, Number of non-orientable coverings of the Klein bottle. FORMULA Multiplicative defined by f(2^k)=2 and f(p^k)=k+1 for k>0 and an odd prime p. 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 *) f[2, e_] := 2; f[p_, e_] := e+1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 15 2020 *) 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 July 29 02:27 EDT 2021. Contains 346340 sequences. (Running on oeis4.)