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A136655
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Product of odd divisors of n.
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6
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1, 1, 3, 1, 5, 3, 7, 1, 27, 5, 11, 3, 13, 7, 225, 1, 17, 27, 19, 5, 441, 11, 23, 3, 125, 13, 729, 7, 29, 225, 31, 1, 1089, 17, 1225, 27, 37, 19, 1521, 5, 41, 441, 43, 11, 91125, 23, 47, 3, 343, 125, 2601, 13, 53, 729, 3025, 7, 3249, 29, 59, 225, 61, 31, 250047, 1, 4225, 1089
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(p) = p if p noncomposite; a(2^n) = 1; a(pq) = p^2 * q^2 when p, q are odd primes.
a(n) = sqrt(n^od(n)/2^ed(n)), where od(n) = number of odd divisors of n = tau(2*n)-tau(n) and ed(n) = number of even divisors of n = 2*tau(n)-tau(2*n). - Vladeta Jovovic, Jun 25 2008
Also a(n) = A007955(A000265(n)). - David Wilson, Jun 26 2008
a(n) = PRODUCT{h == 1 mod 4 and h | n}*PRODUCT{i == 3 mod 4 and i | n}.
a(n) = PRODUCT{j == 1 mod 6 and j | n}*PRODUCT{k == 5 mod 6 and k | n}.
a(n) = A140210(n)*A140211(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 27 2008
a(n) = A007955(n) / A125911(n).
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MAPLE
| with(numtheory); f:=proc(n) local t1, i, k; t1:=divisors(n); k:=1; for i in t1 do if i mod 2 = 1 then k:=k*i; fi; od; k; end; (N. J. A. Sloane)
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CROSSREFS
| Cf. A000265, A000593, A007955, A007956, A078701, A140210-A140215.
Cf. A125911, A126192.
Cf. A001227, A183063.
Sequence in context: A030101 A162742 A081432 * A060819 A089654 A097062
Adjacent sequences: A136652 A136653 A136654 * A136656 A136657 A136658
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KEYWORD
| nonn,easy
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 25 2008
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EXTENSIONS
| More terms from N. J. A. Sloane (njas(AT)research.att.com), Jul 14 2008
Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008 at the suggestion of R. J. Mathar
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