λ
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Atlas › Integer Profiles › Node 31,681,000

31,681,000

23 × 53 × 13 × 2437
Abundant Even Composite

31,681,000 factors as 2^3 × 5^3 × 13 × 2437. Its 64 positive divisors give a proper-divisor sum of 48,187,880, so this integer is abundant. The Collatz stopping time is 188 steps.

Prime Factor Structure

Factorization String 2^3 × 5^3 × 13 × 2437
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 79,868,880
Proper Divisor Sum 48,187,880
Digit Sum / Digital Root 19 (Root: 1)
Adjacent Primes #31680931 ← → #31681007

Radix Representation

Decimal 31681000
Binary 1111000110110100111101000 (25 bits)
Octal 0o170664750
Hexadecimal 0x1E369E8

Divisor Catalog (60 of 64)

1 2 4 5 8 10 13 20 25 26 40 50 52 65 100 104 125 130 200 250 260 325 500 520 650 1,000 1,300 1,625 2,437 2,600 3,250 4,874 6,500 9,748 12,185 13,000 19,496 24,370 31,681 48,740 60,925 63,362 97,480 121,850 126,724 158,405 243,700 253,448 304,625 316,810 487,400 609,250 633,620 792,025 1,218,500 1,267,240 1,584,050 2,437,000 3,168,100 3,960,125

Collatz Trajectory (188 steps to reach 1)

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

31,681,000 15,840,500 7,920,250 3,960,125 11,880,376 5,940,188 2,970,094 1,485,047 4,455,142 2,227,571 6,682,714 3,341,357 10,024,072 5,012,036 2,506,018 1,253,009 3,759,028 1,879,514 939,757 2,819,272 1,409,636 704,818 352,409 1,057,228 528,614 264,307 792,922 396,461 1,189,384 594,692 297,346 148,673 446,020 223,010 111,505 334,516 167,258 83,629 250,888 125,444 62,722 31,361 94,084 47,042 23,521 70,564 35,282 17,641 52,924 26,462 13,231 39,694 19,847 59,542 29,771 89,314 44,657 133,972 66,986 33,493

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