λ
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Atlas › Integer Profiles › Node 40,212,340

40,212,340

22 × 5 × 72 × 37 × 1109
Abundant Even Composite

40,212,340 factors as 2^2 × 5 × 7^2 × 37 × 1109. Its 72 positive divisors give a proper-divisor sum of 60,766,580, so this integer is abundant. The Collatz stopping time is 116 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7^2 × 37 × 1109
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 100,978,920
Proper Divisor Sum 60,766,580
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #40212329 ← → #40212371

Radix Representation

Decimal 40212340
Binary 10011001011001011101110100 (26 bits)
Octal 0o231313564
Hexadecimal 0x2659774

Divisor Catalog (60 of 72)

1 2 4 5 7 10 14 20 28 35 37 49 70 74 98 140 148 185 196 245 259 370 490 518 740 980 1,036 1,109 1,295 1,813 2,218 2,590 3,626 4,436 5,180 5,545 7,252 7,763 9,065 11,090 15,526 18,130 22,180 31,052 36,260 38,815 41,033 54,341 77,630 82,066 108,682 155,260 164,132 205,165 217,364 271,705 287,231 410,330 543,410 574,462

Collatz Trajectory (116 steps to reach 1)

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

40,212,340 20,106,170 10,053,085 30,159,256 15,079,628 7,539,814 3,769,907 11,309,722 5,654,861 16,964,584 8,482,292 4,241,146 2,120,573 6,361,720 3,180,860 1,590,430 795,215 2,385,646 1,192,823 3,578,470 1,789,235 5,367,706 2,683,853 8,051,560 4,025,780 2,012,890 1,006,445 3,019,336 1,509,668 754,834 377,417 1,132,252 566,126 283,063 849,190 424,595 1,273,786 636,893 1,910,680 955,340 477,670 238,835 716,506 358,253 1,074,760 537,380 268,690 134,345 403,036 201,518 100,759 302,278 151,139 453,418 226,709 680,128 340,064 170,032 85,016 42,508

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