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A145737
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a(n) = square part of A145609(n)
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2
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1, 5, 7, 1, 11, 13, 1, 17, 19, 1, 23, 1, 1, 29, 31, 1, 1, 37, 1, 41, 43, 1, 47, 1, 1, 53, 1, 1, 59, 61, 1, 1, 67, 1, 71, 73, 1, 1, 79, 1, 83, 1, 1, 89, 1, 1, 1, 97, 1, 101, 103, 1, 107, 109, 1, 113, 1, 1, 1, 1, 1, 1, 127, 1, 131, 1, 1, 137, 139, 1, 1, 1, 1, 149, 151, 1, 1, 157, 1, 1, 163
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For squarefree parts see A145738. Very similar sequence is A128059.
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FORMULA
| With exception first term is following rule:
a(n)=2n+1 if 2n+1 is prime or 1 in opposite case.
a(n)=Denominator(n!*sum(k^3,k=1..n)/sum(k^2,k=1..n))
=Denominator(n!*3*n*(n+1)/(2*(2*n+1))).[From Gary Detlefs, Oct 18 2011]
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MAPLE
| seq(denom(n!*3*n*(n+1)/(2*(2*n+1))), n=1..81); .[From Gary Detlefs, Oct 18 2011]
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MATHEMATICA
| m = 1; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; b = Sqrt[Numerator[k]] /. Sqrt[_] -> 1; AppendTo[aa, b], {r, 1, 137}]; aa (*Artur Jasinski*)
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CROSSREFS
| A128059, A145609, A145738
Sequence in context: A023571 A160631 A155066 * A108763 A061415 A196847
Adjacent sequences: A145734 A145735 A145736 * A145738 A145739 A145740
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Oct 17 2008
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