λ
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Atlas › Integer Profiles › Node 31,582,040

31,582,040

23 × 5 × 7 × 149 × 757
Abundant Even Composite

31,582,040 factors as 2^3 × 5 × 7 × 149 × 757. Its 64 positive divisors give a proper-divisor sum of 50,281,960, so this integer is abundant. The Collatz stopping time is 126 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 149 × 757
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 81,864,000
Proper Divisor Sum 50,281,960
Digit Sum / Digital Root 23 (Root: 5)
Adjacent Primes #31582037 ← → #31582043

Radix Representation

Decimal 31582040
Binary 1111000011110011101011000 (25 bits)
Octal 0o170363530
Hexadecimal 0x1E1E758

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 149 280 298 596 745 757 1,043 1,192 1,490 1,514 2,086 2,980 3,028 3,785 4,172 5,215 5,299 5,960 6,056 7,570 8,344 10,430 10,598 15,140 20,860 21,196 26,495 30,280 41,720 42,392 52,990 105,980 112,793 211,960 225,586 451,172 563,965 789,551 902,344 1,127,930 1,579,102 2,255,860 3,158,204 3,947,755 4,511,720

Collatz Trajectory (126 steps to reach 1)

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

31,582,040 15,791,020 7,895,510 3,947,755 11,843,266 5,921,633 17,764,900 8,882,450 4,441,225 13,323,676 6,661,838 3,330,919 9,992,758 4,996,379 14,989,138 7,494,569 22,483,708 11,241,854 5,620,927 16,862,782 8,431,391 25,294,174 12,647,087 37,941,262 18,970,631 56,911,894 28,455,947 85,367,842 42,683,921 128,051,764 64,025,882 32,012,941 96,038,824 48,019,412 24,009,706 12,004,853 36,014,560 18,007,280 9,003,640 4,501,820 2,250,910 1,125,455 3,376,366 1,688,183 5,064,550 2,532,275 7,596,826 3,798,413 11,395,240 5,697,620 2,848,810 1,424,405 4,273,216 2,136,608 1,068,304 534,152 267,076 133,538 66,769 200,308

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