λ
Sequence Observatory
Atlas › Integer Profiles › Node 8,440,140

8,440,140

22 × 3 × 5 × 163 × 863
Abundant Even Composite

Starting at 8,440,140, the Collatz iteration reaches 1 after 106 steps. The first transition is 4220070; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 163 × 863
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 23,804,928
Proper Divisor Sum 15,364,788
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #8440139 ← → #8440147

Radix Representation

Decimal 8440140
Binary 100000001100100101001100 (24 bits)
Octal 0o40144514
Hexadecimal 0x80C94C

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 30 60 163 326 489 652 815 863 978 1,630 1,726 1,956 2,445 2,589 3,260 3,452 4,315 4,890 5,178 8,630 9,780 10,356 12,945 17,260 25,890 51,780 140,669 281,338 422,007 562,676 703,345 844,014 1,406,690 1,688,028 2,110,035 2,813,380 4,220,070 8,440,140

Collatz Trajectory (106 steps to reach 1)

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

8,440,140 4,220,070 2,110,035 6,330,106 3,165,053 9,495,160 4,747,580 2,373,790 1,186,895 3,560,686 1,780,343 5,341,030 2,670,515 8,011,546 4,005,773 12,017,320 6,008,660 3,004,330 1,502,165 4,506,496 2,253,248 1,126,624 563,312 281,656 140,828 70,414 35,207 105,622 52,811 158,434 79,217 237,652 118,826 59,413 178,240 89,120 44,560 22,280 11,140 5,570 2,785 8,356 4,178 2,089 6,268 3,134 1,567 4,702 2,351 7,054 3,527 10,582 5,291 15,874 7,937 23,812 11,906 5,953 17,860 8,930

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