|
|
|
|
|
|
|
|
|
#35 by Wesley Ivan Hurt at Sat Dec 12 00:16:42 EST 2015
|
|
|
|
|
|
|
|
#34 by Jon E. Schoenfield at Fri Dec 11 22:09:11 EST 2015
|
|
|
|
|
|
|
|
#33 by Jon E. Schoenfield at Fri Dec 11 22:09:08 EST 2015
|
|
| COMMENTS
|
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.)
|
|
| STATUS
|
approved
editing
|
|
|
|
|
|
|
#32 by Ralf Stephan at Wed Dec 11 05:21:13 EST 2013
|
|
|
|
|
|
|
|
#31 by José María Grau Ribas at Tue Dec 10 15:26:55 EST 2013
|
|
|
|
|
|
Discussion
|
| Wed Dec 11
| 05:20
| Ralf Stephan: Maybe also submit the complement.
|
|
|
|
|
|
|
#30 by José María Grau Ribas at Tue Dec 10 15:26:40 EST 2013
|
|
| COMMENTS
|
The asymptotic density is in [0.7880, 7747,0.8079812570].
|
|
| CROSSREFS
|
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).
|
|
| STATUS
|
proposed
editing
|
|
|
|
|
|
|
#29 by Jonathan Sondow at Tue Dec 10 15:09:32 EST 2013
|
|
|
|
|
|
|
|
#28 by Jonathan Sondow at Tue Dec 10 15:09:29 EST 2013
|
|
| COMMENTS
|
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.)
|
|
|
|
|
|
|
#27 by José María Grau Ribas at Mon Dec 09 10:12:17 EST 2013
|
|
| COMMENTS
|
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.
|
|
| STATUS
|
approved
editing
|
|
|
|
|
|
|
#26 by Charles R Greathouse IV at Mon Oct 21 09:41:49 EDT 2013
|
|
|
|
|
|
|
