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A086535
Product of numbers obtained by adding one to the odd divisors of n and subtracting 1 from the even divisors.
1
2, 2, 8, 6, 12, 40, 16, 42, 80, 108, 24, 1320, 28, 208, 768, 630, 36, 6800, 40, 6156, 1408, 504, 48, 212520, 312, 700, 2240, 16848, 60, 1002240, 64, 19530, 3264, 1188, 3456, 7854000, 76, 1480, 4480, 1680588, 84, 3752320, 88, 65016, 353280, 2160, 96
OFFSET
1,1
FORMULA
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.
a(p) = 2(p+1), a(p^r) = (p^r +1)*a(p^(r-1)) where p is an odd prime.
EXAMPLE
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.
MATHEMATICA
Table[Times@@(If[OddQ[#], #+1, #-1]&/@Divisors[n]), {n, 50}] (* Harvey P. Dale, Sep 25 2022 *)
PROG
(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
CROSSREFS
Sequence in context: A371937 A119999 A061828 * A344601 A067436 A285114
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Aug 18 2003
EXTENSIONS
More terms from David Wasserman, Mar 15 2005
STATUS
approved