# Polya's Conjecture: more odd #factors numbers

Hans Havermann hahaj at rogers.com
Thu Jun 20 17:43:54 CEST 2002

```>>> n  | 2  3  4  5  6  7  8  9  10  11  12
>>> o/e | o  o  e  o  e  o  o  e   e   o   o,   o = oddly,  e = evenly
>>> #o-#e  1  2  1  2  1  2  3  2   1   2   3

>> [snip]

>>> Lehman confirmed Haselgrove's calculations and by direct calculation
>>> found a smaller counterexample  #o - #e = -1 for  n = 906180359, and
>>> found further negative values over a considerable number of ranges of
>>> n  in the intervals  906170000  to  906200000  and  906470000  to
>>> 906500000.

More specifically (assuming #o - #e == +1 for  n = 906180357), the zero
points (#o-#e[[n]] == 0) where a sign-change occurs (#o-#e[[n-1]] +
#o-#e[[n+1]] == 0, as opposed this the sum being +2 or -2) are:

906180358, 906180376, 906180390, 906180520, 906180524, 906180534, 906180536,
906192698, 906192846, 906192966, 906192970, 906192972, 906192978, 906193234,
906193244, 906193248, 906193302, 906193304, 906193418, 906193420, 906193464,
906193466, 906193474, 906193478, 906194930, 906194946, 906194948, 906194968,
906194978, 906194980, 906195098, 906195100, 906195108, 906195152, 906195296,
906195986, 906195988, 906195990, 906196008, 906196016, 906196044, 906196072,
906196076, 906196092, 906196098, 906208714, 906208730, 906208732, 906209040,
906209064, 906209066, 906209224, 906209226, 906209228, 906209232, 906209238,
906209240, 906209272, 906209282, 906477702, 906477734, 906477812, 906477866,
906477906, 906477928, 906486640, 906486804, 906486808, 906486816, 906486832,
906486842, 906486856, 906486908, 906486914, 906486916, 906487002, 906487004,
906487066, 906487068, 906487078, 906487084, 906487102, 906487184, 906487206,
906487258, 906487264, 906487270, 906487288, 906487932, 906487934, 906487936,
906487938, 906487948, 906488004, 906488006, 906488010, 906488022, 906488068,
906488076, 906488080, ...

```