A086535 Product of numbers obtained by adding one to the odd divisors of n and subtracting 1 from the even divisors.

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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.

Maple

f:= proc(n) local d;
  mul(`if`(d::odd, d+1, d-1), d=numtheory:-divisors(n))
end proc:
map(f, [$1..100]); # Robert Israel, Dec 25 2024

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: A119999 A061828 A379796 * A344601 A067436 A285114

Adjacent sequences: A086532 A086533 A086534 * A086536 A086537 A086538

Keyword

nonn,easy,look

Author

Amarnath Murthy, Aug 18 2003

Extensions

More terms from David Wasserman, Mar 15 2005

Status

approved