λ
Sequence Observatory
Atlas › Integer Profiles › Node 1,089,312

1,089,312

25 × 3 × 7 × 1621
Abundant Even Composite

Starting at 1,089,312, the Collatz iteration reaches 1 after 165 steps. The first transition is 544656; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3 × 7 × 1621
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 3,269,952
Proper Divisor Sum 2,180,640
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #1089299 ← → #1089313

Radix Representation

Decimal 1089312
Binary 100001001111100100000 (21 bits)
Octal 0o4117440
Hexadecimal 0x109F20

Divisor Catalog (48)

1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 56 84 96 112 168 224 336 672 1,621 3,242 4,863 6,484 9,726 11,347 12,968 19,452 22,694 25,936 34,041 38,904 45,388 51,872 68,082 77,808 90,776 136,164 155,616 181,552 272,328 363,104 544,656 1,089,312

Collatz Trajectory (165 steps to reach 1)

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

1,089,312 544,656 272,328 136,164 68,082 34,041 102,124 51,062 25,531 76,594 38,297 114,892 57,446 28,723 86,170 43,085 129,256 64,628 32,314 16,157 48,472 24,236 12,118 6,059 18,178 9,089 27,268 13,634 6,817 20,452 10,226 5,113 15,340 7,670 3,835 11,506 5,753 17,260 8,630 4,315 12,946 6,473 19,420 9,710 4,855 14,566 7,283 21,850 10,925 32,776 16,388 8,194 4,097 12,292 6,146 3,073 9,220 4,610 2,305 6,916

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