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#35 by Wesley Ivan Hurt at Sat Dec 12 00:16:42 EST 2015
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#34 by Jon E. Schoenfield at Fri Dec 11 22:09:11 EST 2015
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#33 by Jon E. Schoenfield at Fri Dec 11 22:09:08 EST 2015
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| COMMENTS
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The numbers k = 1, 2, 6, 42, 1806, 47058, 2214502422, 8490421583559688410706771261086 = A230311 are the only values of k such that the set {n: A031971(k*n) == n (mod k*n)} is non-emptynonempty. Its smallest element is n = 1, 1, 1, 1, 1, 5, 5, 39607528021345872635 = A231409. (Comment corrected and expanded by Jonathan Sondow, Dec 10 2013.)
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| STATUS
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approved
editing
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#32 by Ralf Stephan at Wed Dec 11 05:21:13 EST 2013
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#31 by José María Grau Ribas at Tue Dec 10 15:26:55 EST 2013
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Discussion
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Wed Dec 11
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| Ralf Stephan: Maybe also submit the complement.
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#30 by José María Grau Ribas at Tue Dec 10 15:26:40 EST 2013
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| COMMENTS
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The asymptotic density is in [0.7880, 7747,0.8079812570].
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| CROSSREFS
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Cf. A031971, A231409.
Cf. A014117A231562 (numbers n such that A031971(8490421583559688410706771261086*n) == n)==1 (mod 8490421583559688410706771261086*n)).
Cf. A229312 (numbers n such that A031971(47058*n) == n (mod 47058*n)).
Cf. A229313 (numbers n such that A031971(47058*n) <> n (mod 47058*n)).
Cf. A054377 (primary pseudoperfect numbers).
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| STATUS
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proposed
editing
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#29 by Jonathan Sondow at Tue Dec 10 15:09:32 EST 2013
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#28 by Jonathan Sondow at Tue Dec 10 15:09:29 EST 2013
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| COMMENTS
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The numbers in k = 1, 2, 6, 42, 1806, 47058, 2214502422, 8490421583559688410706771261086 = A230311 are the only values of k such that the set {n :: A031971(k*n)== ) == n (mod k*n)} is non-empty.. Its smallest element is n = 1, 1, 1, 1, 1, 5, 5, 39607528021345872635 = A231409. (Comment corrected and expanded by _Jonathan Sondow_, Dec 10 2013.)
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#27 by José María Grau Ribas at Mon Dec 09 10:12:17 EST 2013
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| COMMENTS
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The numbers {1, 2, 6, 42, 1806} in A230311 are the only values of k such that the set {n: :A031971(k*n) == )== n (mod k*n) )} is non-empty.
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| STATUS
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approved
editing
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#26 by Charles R Greathouse IV at Mon Oct 21 09:41:49 EDT 2013
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