Numbers 530,000s

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530,881

[Math.]  A Carmichael number: 530,881 = 13×97×421.

 

531,441

[Math.]  531,441 = (5+31+44+1)3 = 813

             531,441 = (5+3+14+4+1)4 = 274.

 

531,487

[Math.]  124,367,958 = 627×198354 = 9×26×531487.

 

533,170

[Math.]  :  217,930,248,900 = (217,930+248,900)2 = 466,8302 and 284,270,248,900 = (284270+248900)2 = 533,1702 and 466,380+533,170 = 1,000,000.

 

533,417 & 533,418

[Math.]  533,417 = 1!2+2!2+3!2+4!2+5!2+6!2.

             533,418 = 0!2+1!2+2!2+3!2+4!2+5!2+6!2.

 

538,461

[Math.]  213,018,248,521 = (213,018+248,521)2 = 461,5392 and

289,940,248,521 = (289940+248521)2 = 538,4612 and 461,539+538,461 = 1,000,000.

 

[Math.]  The 6-digit period of the rational number 1/13 = 0.076923076923… or 0.076923. Its multiple by 13 is 999,999.  Then,   076,923×n = abc,def,ghi,jkl and

abc,def+ghi,jkl = 076,923, if n  = 13t+1

abc,def+ghi,jkl = 692,307, if n  = 13t+9

abc,def+ghi,jkl = 230,769, if n  = 13t+3

abc,def+ghi,jkl = 769,230, if n  = 13t+10

abc,def+ghi,jkl = 307,692, if n  = 13t+4

abc,def+ghi,jkl = 923,076, if n  = 13t+12

 for t = 0 to 76,922, and in fact abc,edf = t.  The results are digit-rotations of 076,923.

            And 076,923×n = abc,def,ghi,jkl &

abc,def+ghi,jkl = 153,846, if n  = 13t+2

abc,def+ghi,jkl = 538,461, if n  = 13t+7

abc,def+ghi,jkl = 384,615, if n  = 13t+5

abc,def+ghi,jkl = 615,384, if n  = 13t+8

abc,def+ghi,jkl = 461,538, if n  = 13t+6

abc,def+ghi,jkl = 846,153, if n  = 13t+11

for t = 0 to 76,922, and in fact abc,edf = t.  The results are digit-rotations of 076,923×2 = 153,846. It is the period of the rational number 2/13 = 0.153846153846… or 0.153846), and the sums of first and last 3-digit numbers are always 999.