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A161493
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Positive integers, k, for which Mod[k,d(k)] and k have opposite (odd/even) parity, where d(k) is the number of divisors of k
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1
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1, 4, 9, 16, 64, 100, 144, 196, 225, 324, 441, 484, 576, 625, 676, 900, 1024, 1089, 1296, 1521, 1764, 1936, 2025, 2116, 2304, 2601, 3136, 3249, 3364, 3844, 4096, 4225, 4356, 4761, 4900, 5625, 5776, 6084, 6400, 6561, 6724, 7396, 7569, 8649, 8836, 9216, 9801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| It appears that the sequence {a(n)} consists entirely of squares. (This has been verified to a(431)=998001=999^2.)
A number k appears in the sequence if and only if k is a square and floor(k/d(k)) is odd. Ths is because Mod(k,d(k) = k - d(k) * floor(k/d(k)) and d(k) is odd if and only if k is square. [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 12 2009]
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EXAMPLE
| k=4 has three divisors, so Mod[4,d(4)]=1, which is odd. But 4 is even. Therefore 4 is a term of the sequence.
k=25 has three divisors, so Mod[25,d(25)]=1, which is odd. 25 is also odd. Therefore 25 is not a term of the sequence.
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PROG
| (PARI) for(i=1, 999, k=i^2; if(floor(k/numdiv(k))%2, print1(k, ", "))) [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 12 2009]
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CROSSREFS
| Sequence in context: A164840 A023110 A073723 * A030075 A038784 A038239
Adjacent sequences: A161490 A161491 A161492 * A161494 A161495 A161496
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Jun 11 2009
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