Search: id:A145378
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%I A145378
%S A145378 1,2,5,7,7,10,9,20,18,14,13,35,15,18,35,49,19,36,21,49,45,26,25,100,38,
%T A145378 30,58,63,31,70,33,110,65,38,63,126,39,42,75,140,43,90,45,91,126,50,49,
%U A145378 245,66,76,95,105,55,116,91,180,105,62,61,245,63,66,162,235,105,130,69
%N A145378 a(n) = Sum_{d|n} sigma(d) - 2*Sum_{2c|n} sigma(c) + 4*Sum_{4b|n} sigma(b).
%D A145378 J. S. Rutherford, The enumeration and symmetry-significant properties 
               of derivative lattices, Acta Cryst. A48 (1992), 500-508. See g(n).
%p A145378 with(numtheory); g:=proc(n) local d,c,b,t0,t1,t2,t3;
%p A145378 t1:=divisors(n);
%p A145378 t0:=add( sigma(d), d in t1);
%p A145378 t2:=0; for d in t1 do if d mod 2 = 0 then t2:=t2+sigma(d/2); fi; od:
%p A145378 t3:=0; for d in t1 do if d mod 4 = 0 then t3:=t3+sigma(d/4); fi; od:
%p A145378 t0-2*t2+4*t3; end;
%p A145378 [seq(g(n),n=1..100)];
%Y A145378 Sequence in context: A021392 A131688 A096624 this_sequence A069887 A120303 
               A093413
%Y A145378 Adjacent sequences: A145375 A145376 A145377 this_sequence A145379 A145380 
               A145381
%K A145378 nonn
%O A145378 1,2
%A A145378 N. J. A. Sloane (njas(AT)research.att.com), Mar 12 2009

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