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Search: id:A086535
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| A086535 |
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Product of numbers obtained by adding one to the odd divisors of n and subtracting 1 from the even divisors. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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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.
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EXAMPLE
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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.
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PROGRAM
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(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]); (Wasserman)
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CROSSREFS
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Sequence in context: A103238 A119999 A061828 this_sequence A067436 A071418 A064862
Adjacent sequences: A086532 A086533 A086534 this_sequence A086536 A086537 A086538
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KEYWORD
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nonn,easy
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 18 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 15 2005
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