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A216780
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Numbers n such that numerator(sigma(n)/n) and denominator(sigma(n)/n) are both odd.
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5
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1, 9, 10, 12, 25, 26, 34, 44, 49, 56, 58, 74, 76, 81, 82, 90, 106, 120, 121, 122, 146, 169, 172, 178, 184, 194, 202, 216, 218, 225, 226, 234, 236, 260, 268, 274, 289, 298, 300, 306, 312, 314, 332, 340, 346, 361, 362, 386, 394, 396, 408, 428, 440, 441, 458
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OFFSET
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1,2
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COMMENTS
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a(n) contains odd squares (A016754), 3-perfect numbers (A005820) and 5-perfect numbers (A046060).
This is also the sequence of numbers x such that A243473(x) is even. - Michel Marcus, Jun 06 2014
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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EXAMPLE
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sigma(10)/10 = 9/5; both 9 and 5 are odd, so 10 is in the sequence.
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MATHEMATICA
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Select[Range[500], OddQ[Numerator[DivisorSigma[1, #]/#]] && OddQ[Denominator[DivisorSigma[1, #]/#]] &] (* Alonso del Arte, Sep 16 2012 *)
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PROG
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(PARI) ooab(k) = {for (i=1, k, ab = sigma(i)/i; if ((numerator(ab) % 2 == 1) && (denominator(ab) % 2 == 1), print1(i, ", ")); ); }
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CROSSREFS
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Cf. A216781, A216782, A016754, A005820, A046060.
Sequence in context: A156345 A078390 A354038 * A279731 A037408 A178680
Adjacent sequences: A216777 A216778 A216779 * A216781 A216782 A216783
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KEYWORD
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nonn,easy
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AUTHOR
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Michel Marcus, Sep 16 2012
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STATUS
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approved
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