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Atlas › Integer Profiles › Node 31,727,722

31,727,722

2 × 132 × 37 × 43 × 59
Deficient Even Composite

31,727,722 factors as 2 × 13^2 × 37 × 43 × 59. Its 48 positive divisors give a proper-divisor sum of 23,347,958, so this integer is deficient. The Collatz stopping time is 126 steps.

Prime Factor Structure

Factorization String 2 × 13^2 × 37 × 43 × 59
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 55,075,680
Proper Divisor Sum 23,347,958
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #31727713 ← → #31727737

Radix Representation

Decimal 31727722
Binary 1111001000010000001101010 (25 bits)
Octal 0o171020152
Hexadecimal 0x1E4206A

Divisor Catalog (48)

1 2 13 26 37 43 59 74 86 118 169 338 481 559 767 962 1,118 1,534 1,591 2,183 2,537 3,182 4,366 5,074 6,253 7,267 9,971 12,506 14,534 19,942 20,683 28,379 32,981 41,366 56,758 65,962 93,869 187,738 268,879 368,927 428,753 537,758 737,854 857,506 1,220,297 2,440,594 15,863,861 31,727,722

Collatz Trajectory (126 steps to reach 1)

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

31,727,722 15,863,861 47,591,584 23,795,792 11,897,896 5,948,948 2,974,474 1,487,237 4,461,712 2,230,856 1,115,428 557,714 278,857 836,572 418,286 209,143 627,430 313,715 941,146 470,573 1,411,720 705,860 352,930 176,465 529,396 264,698 132,349 397,048 198,524 99,262 49,631 148,894 74,447 223,342 111,671 335,014 167,507 502,522 251,261 753,784 376,892 188,446 94,223 282,670 141,335 424,006 212,003 636,010 318,005 954,016 477,008 238,504 119,252 59,626 29,813 89,440 44,720 22,360 11,180 5,590

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