λ
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Atlas › Integer Profiles › Node 3,206,742

3,206,742

2 × 3 × 7 × 112 × 631
Abundant Even Composite

Starting at 3,206,742, the Collatz iteration reaches 1 after 120 steps. The first transition is 1603371; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 11^2 × 631
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 8,069,376
Proper Divisor Sum 4,862,634
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #3206741 ← → #3206747

Radix Representation

Decimal 3206742
Binary 1100001110111001010110 (22 bits)
Octal 0o14167126
Hexadecimal 0x30EE56

Divisor Catalog (48)

1 2 3 6 7 11 14 21 22 33 42 66 77 121 154 231 242 363 462 631 726 847 1,262 1,694 1,893 2,541 3,786 4,417 5,082 6,941 8,834 13,251 13,882 20,823 26,502 41,646 48,587 76,351 97,174 145,761 152,702 229,053 291,522 458,106 534,457 1,068,914 1,603,371 3,206,742

Collatz Trajectory (120 steps to reach 1)

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

3,206,742 1,603,371 4,810,114 2,405,057 7,215,172 3,607,586 1,803,793 5,411,380 2,705,690 1,352,845 4,058,536 2,029,268 1,014,634 507,317 1,521,952 760,976 380,488 190,244 95,122 47,561 142,684 71,342 35,671 107,014 53,507 160,522 80,261 240,784 120,392 60,196 30,098 15,049 45,148 22,574 11,287 33,862 16,931 50,794 25,397 76,192 38,096 19,048 9,524 4,762 2,381 7,144 3,572 1,786 893 2,680 1,340 670 335 1,006 503 1,510 755 2,266 1,133 3,400

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