Search: id:A046897
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%I A046897
%S A046897 1,3,4,3,6,12,8,3,13,18,12,12,14,24,24,3,18,39,20,18,32,36,24,12,31,42,
%T A046897 40,24,30,72,32,3,48,54,48,39,38,60,56,18,42,96,44,36,78,72,48,12,57,93,
%U A046897 72,42,54,120,72,24,80,90,60,72,62,96,104,3,84,144,68,54,96,144,72
%N A046897 Sum of divisors of n that are not divisible by 4.
%D A046897 P. A. MacMahon, Combinatory Analysis, Cambridge Univ. Press, London and 
               New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 31, Article 
               273.
%F A046897 a(n) = (-1)^(n+1)*Sum_{d divides n} (-1)^(n/d+d)*d. Multiplicative with 
               a(2^e) = 3, a(p^e) = (p^(e+1)-1)/(p-1) for an odd prime p. - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Sep 10 2002
%F A046897 G.f.: Sum_{k>0} x^k/(1+(-x)^k)^2, or Sum_{k>0} k*x^k/(1+(-x)^k). - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Dec 16 2002
%F A046897 Expansion of (1 - phi(q)^4) / 8 in powers of q where phi() is a Ramanujan 
               theta function. - Michael Somos, Jan 25 2008
%F A046897 Equals inverse Mobius transform (A051731) of "count, 4*n = 0": (1, 2, 
               3, 0, 5, 6, 7, 0,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jul 03 2008
%e A046897 q + 3*q^2 + 4*q^3 + 3*q^4 + 6*q^5 + 12*q^6 + 8*q^7 + 3*q^8 + 13*q^9 + 
               ...
%o A046897 (PARI) a(n)=if(n<1,0,sumdiv(n,d,if(d%4,d)))
%Y A046897 a(n)=A000118(n)/8, n>0. Cf. A069733.
%Y A046897 Cf. A051731.
%Y A046897 Sequence in context: A061800 A048250 A073181 this_sequence A109506 A000113 
               A069915
%Y A046897 Adjacent sequences: A046894 A046895 A046896 this_sequence A046898 A046899 
               A046900
%K A046897 nonn,mult
%O A046897 1,2
%A A046897 N. J. A. Sloane (njas(AT)research.att.com).

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