λ
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6,138,540

22 × 32 × 5 × 67 × 509
Abundant Even Composite

6,138,540 factors as 2^2 × 3^2 × 5 × 67 × 509. Its 72 positive divisors give a proper-divisor sum of 12,796,740, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 5 × 67 × 509
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 18,935,280
Proper Divisor Sum 12,796,740
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #6138523 ← → #6138557

Radix Representation

Decimal 6138540
Binary 10111011010101010101100 (23 bits)
Octal 0o27325254
Hexadecimal 0x5DAAAC

Divisor Catalog (60 of 72)

1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 67 90 134 180 201 268 335 402 509 603 670 804 1,005 1,018 1,206 1,340 1,527 2,010 2,036 2,412 2,545 3,015 3,054 4,020 4,581 5,090 6,030 6,108 7,635 9,162 10,180 12,060 15,270 18,324 22,905 30,540 34,103 45,810 68,206 91,620 102,309 136,412 170,515 204,618

Collatz Trajectory (196 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

6,138,540 3,069,270 1,534,635 4,603,906 2,301,953 6,905,860 3,452,930 1,726,465 5,179,396 2,589,698 1,294,849 3,884,548 1,942,274 971,137 2,913,412 1,456,706 728,353 2,185,060 1,092,530 546,265 1,638,796 819,398 409,699 1,229,098 614,549 1,843,648 921,824 460,912 230,456 115,228 57,614 28,807 86,422 43,211 129,634 64,817 194,452 97,226 48,613 145,840 72,920 36,460 18,230 9,115 27,346 13,673 41,020 20,510 10,255 30,766 15,383 46,150 23,075 69,226 34,613 103,840 51,920 25,960 12,980 6,490

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