[seqfan] Re: Pairs Occurring Only Once Among # Of Divisors

Richard Mathar mathar at strw.leidenuniv.nl
Fri Jun 26 20:22:01 CEST 2009


jb> Jack Brennen wrote:
jb>[1, 2, 3, 4, 8, 15, 16, 24, 35, 48, 63, 64, 80, 99, 288, 528, 575, 624,
jb>728, 960, 1023, 1024, 1088, 1295, 2303, 2400, 4095, 4096, 5328, 6399,
jb>6723, 9408, 9999, 14640, 15624, 28223, 36863, 38415, 46655, 50175,
jb>50624, 57121, 59048, 59049, 65535, 65536, 71824, 82944, 83520, 117648,
jb>130320, 146688, 250000, 262143, 262144, 263168, 279840, 331775, 421200,
jb>529983, 531440, 531441, 589824, 640000, 641600, 651249, 746495, 746496,
jb>777924, 860624, 861183, 923520, 937024, 1000000]
jb>
jb>Some of these aren't in the sequence, they just didn't hit a match
jb>before 10^8.  For instance, 1000000 is matched by 94^6, which didn't
jb>take long to find.
jb> ...
jb> I'm currently searching for the smallest match for 860624, it's
jb> probably out there somewhere... :)
jb
jb>30 == numdiv(150309999  ) == numdiv(860624  )
jb>50 == numdiv(150309999+1) == numdiv(860624+1)


tdn> Tony D. Noe wrote:
tdn> 71824 isn't in the sequence because it is matched by  868834576
tdn> 82944 isn't in the sequence because it is matched by 1686498489

250000 is absent because it's matched by 2368574224 .
262144 is absent because it's matched by 387420489 .
421200 is absent because it's matched by 262472400 and 1008253008
589824 is absent because it's matched by 59520385024 and 261358157824
641600 is absent because it's matched by 12408400448
651249 is absent because it's matched by 290941249 and 321951249
746496 is absent because it's matched by 4942652416 and 151588750336 and 2131918594671616
777924 is absent because it's matched by 410791824 and 1983099024
861183 is absent because it's matched by 369869823 and 1063281663 and 7034512383 and 8665375743
937024 is absent because it's matched by 886133824 and 64537845849 and 169935221824 and 384758443521 and 873116441649

I've updated the script in
http://www.strw.leidenuniv.nl/~mathar/progs/a161460.pdf
with proofs that have been posted here and with proofs on 728 and 57121.

Richard Mathar




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