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Atlas › Integer Profiles › Node 31,821,740

31,821,740

22 × 5 × 41 × 151 × 257
Abundant Even Composite

31,821,740 factors as 2^2 × 5 × 41 × 151 × 257. Its 48 positive divisors give a proper-divisor sum of 37,355,284, so this integer is abundant. The Collatz stopping time is 69 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 41 × 151 × 257
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 69,177,024
Proper Divisor Sum 37,355,284
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #31821733 ← → #31821743

Radix Representation

Decimal 31821740
Binary 1111001011000111110101100 (25 bits)
Octal 0o171307654
Hexadecimal 0x1E58FAC

Divisor Catalog (48)

1 2 4 5 10 20 41 82 151 164 205 257 302 410 514 604 755 820 1,028 1,285 1,510 2,570 3,020 5,140 6,191 10,537 12,382 21,074 24,764 30,955 38,807 42,148 52,685 61,910 77,614 105,370 123,820 155,228 194,035 210,740 388,070 776,140 1,591,087 3,182,174 6,364,348 7,955,435 15,910,870 31,821,740

Collatz Trajectory (69 steps to reach 1)

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

31,821,740 15,910,870 7,955,435 23,866,306 11,933,153 35,799,460 17,899,730 8,949,865 26,849,596 13,424,798 6,712,399 20,137,198 10,068,599 30,205,798 15,102,899 45,308,698 22,654,349 67,963,048 33,981,524 16,990,762 8,495,381 25,486,144 12,743,072 6,371,536 3,185,768 1,592,884 796,442 398,221 1,194,664 597,332 298,666 149,333 448,000 224,000 112,000 56,000 28,000 14,000 7,000 3,500 1,750 875 2,626 1,313 3,940 1,970 985 2,956 1,478 739 2,218 1,109 3,328 1,664 832 416 208 104 52 26

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