λ
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Atlas › Integer Profiles › Node 37,806,790

37,806,790

2 × 5 × 7 × 71 × 7607
Abundant Even Composite

37,806,790 factors as 2 × 5 × 7 × 71 × 7607. Its 32 positive divisors give a proper-divisor sum of 41,072,954, so this integer is abundant. The Collatz stopping time is 227 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 71 × 7607
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 78,879,744
Proper Divisor Sum 41,072,954
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #37806721 ← → #37806803

Radix Representation

Decimal 37806790
Binary 10010000001110001011000110 (26 bits)
Octal 0o220161306
Hexadecimal 0x240E2C6

Divisor Catalog (32)

1 2 5 7 10 14 35 70 71 142 355 497 710 994 2,485 4,970 7,607 15,214 38,035 53,249 76,070 106,498 266,245 532,490 540,097 1,080,194 2,700,485 3,780,679 5,400,970 7,561,358 18,903,395 37,806,790

Collatz Trajectory (227 steps to reach 1)

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

37,806,790 18,903,395 56,710,186 28,355,093 85,065,280 42,532,640 21,266,320 10,633,160 5,316,580 2,658,290 1,329,145 3,987,436 1,993,718 996,859 2,990,578 1,495,289 4,485,868 2,242,934 1,121,467 3,364,402 1,682,201 5,046,604 2,523,302 1,261,651 3,784,954 1,892,477 5,677,432 2,838,716 1,419,358 709,679 2,129,038 1,064,519 3,193,558 1,596,779 4,790,338 2,395,169 7,185,508 3,592,754 1,796,377 5,389,132 2,694,566 1,347,283 4,041,850 2,020,925 6,062,776 3,031,388 1,515,694 757,847 2,273,542 1,136,771 3,410,314 1,705,157 5,115,472 2,557,736 1,278,868 639,434 319,717 959,152 479,576 239,788

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