λ
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Atlas › Integer Profiles › Node 8,691,968

8,691,968

28 × 19 × 1787
Abundant Even Composite

Starting at 8,691,968, the Collatz iteration reaches 1 after 150 steps. The first transition is 4345984; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^8 × 19 × 1787
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 18,273,360
Proper Divisor Sum 9,581,392
Digit Sum / Digital Root 47 (Root: 2)
Adjacent Primes #8691961 ← → #8691971

Radix Representation

Decimal 8691968
Binary 100001001010000100000000 (24 bits)
Octal 0o41120400
Hexadecimal 0x84A100

Divisor Catalog (36)

1 2 4 8 16 19 32 38 64 76 128 152 256 304 608 1,216 1,787 2,432 3,574 4,864 7,148 14,296 28,592 33,953 57,184 67,906 114,368 135,812 228,736 271,624 457,472 543,248 1,086,496 2,172,992 4,345,984 8,691,968

Collatz Trajectory (150 steps to reach 1)

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

8,691,968 4,345,984 2,172,992 1,086,496 543,248 271,624 135,812 67,906 33,953 101,860 50,930 25,465 76,396 38,198 19,099 57,298 28,649 85,948 42,974 21,487 64,462 32,231 96,694 48,347 145,042 72,521 217,564 108,782 54,391 163,174 81,587 244,762 122,381 367,144 183,572 91,786 45,893 137,680 68,840 34,420 17,210 8,605 25,816 12,908 6,454 3,227 9,682 4,841 14,524 7,262 3,631 10,894 5,447 16,342 8,171 24,514 12,257 36,772 18,386 9,193

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