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Leyland numbers
A number that can be written as ab + ba for a, b > 1. more

The Leyland numbers up to 1015 :
8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124, 1649, 2169, 2530, 4240, 5392, 6250, 7073, 8361, 16580, 18785, 20412, 23401, 32993, 60049, 65792, 69632, 93312, 94932, 131361, 178478, 262468, 268705, 397585, 423393, 524649, 533169, 1048976, 1058576, 1596520, 1647086, 1941760, 2012174, 2097593, 4194788, 4208945, 4785713, 7861953, 8389137, 9865625, 10609137, 14352282, 16777792, 16797952, 33554432, 33555057, 43050817, 45136576, 48989176, 61466176, 67109540, 67137425, 129145076, 134218457, 177264449, 244389457, 268436240, 268473872, 292475249, 364568617, 387426321, 536871753, 774840978, 1073742724, 1073792449, 1162268326, 1173741824, 1221074418, 1996813914, 2147484609, 2179768320, 3486792401, 4294968320, 4295032832, 4486784401, 6104053449, 8589935681, 8804293473, 10460362464, 13065520825, 13877119009, 17179870340, 17179952705, 20000000000, 30518337500, 31381070257, 33739007300, 34359739593, 68719478032, 68719581712, 69149458432, 78371693632, 94143190994, 96951758924, 125937424601, 137438954841, 152588939201, 274877908388, 274878037265, 282429550305, 287589316833, 470196375201, 549755815409, 550571544609, 570623341222, 678328486353, 762940872982, 847288625068, 1061917364224, 1099511629376, 1099511787776, 2199023257233, 2541865845905, 2552470327702, 2821126684672, 3814699155193, 3881436747409, 4398046512868, 4398046705585, 4399522300160, 4747732369318, 7625597504670, 8796093024057, 10137858491849, 16926683582305, 17592186046352, 17592186278672, 17832200896512, 19073488804224, 22876792476913, 22897453501745, 33233199005057, 35184372090857, 35186934979457, 36314872537968, 68630377389272, 70368744179780, 70368744457505, 95367434840625, 100289254654976, 101559990680640, 130291290501553, 140737488357537, 205891132121649, 205929575454024, 232630924325880, 281474976712960, 281474977042432, 281479271677952, 383799398752905, 476837162287226, 562949953423713, 605750213184506, 609359787056377, 617673396313738.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 116412 values, from 8 to 101000).

n\r 0  1 
25830358109 2 
3323754139842639 3 
44394758109143560 4 
52584823881281231877019790 5 
6126621890123144197132249719495 6 
715164182052245517846126361691513191 7 
83599058109717507957071810 8 
9193773928097666498106197666500105723107 9 
10141271138516482116748102117211249611641709611688 10 
1195191020213882969912051112451100986479484908811586

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.