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%I #10 Sep 24 2023 04:30:47
%S 2,2,8,6,12,40,16,42,80,108,24,1320,28,208,768,630,36,6800,40,6156,
%T 1408,504,48,212520,312,700,2240,16848,60,1002240,64,19530,3264,1188,
%U 3456,7854000,76,1480,4480,1680588,84,3752320,88,65016,353280,2160,96
%N Product of numbers obtained by adding one to the odd divisors of n and subtracting 1 from the even divisors.
%F a(n) = (Ea-1)*(Eb-1)*(Ec-1)* ...*(Oa+1)*(Ob+1)*(Oc+1)..., where Ea, Eb, Ec, ... and Oa, Ob, Oc, ... are respectively the even and odd divisors of n.
%F a(p) = 2(p+1), a(p^r) = (p^r +1)*a(p^(r-1)) where p is an odd prime.
%e a(14) = 208. The divisors of 14 are 1,2,7 and 14 and the corresponding numbers obtained are 2,1,8 and 13 whose product is 208.
%t Table[Times@@(If[OddQ[#],#+1,#-1]&/@Divisors[n]),{n,50}] (* _Harvey P. Dale_, Sep 25 2022 *)
%o (PARI) a(n) = local(d); d = divisors(n); for (i = 1, length(d), if (d[i]%2, d[i]++, d[i]--)); prod(i = 1, length(d), d[i]); \\ _David Wasserman_, Mar 15 2005
%K nonn,easy
%O 1,1
%A _Amarnath Murthy_, Aug 18 2003
%E More terms from _David Wasserman_, Mar 15 2005
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