λ
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Atlas › Integer Profiles › Node 1,217,744

1,217,744

24 × 112 × 17 × 37
Abundant Even Composite

Starting at 1,217,744, the Collatz iteration reaches 1 after 204 steps. The first transition is 608872; the starting value is even with 60 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 11^2 × 17 × 37
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 2,820,132
Proper Divisor Sum 1,602,388
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #1217731 ← → #1217753

Radix Representation

Decimal 1217744
Binary 100101001010011010000 (21 bits)
Octal 0o4512320
Hexadecimal 0x1294D0

Divisor Catalog (60)

1 2 4 8 11 16 17 22 34 37 44 68 74 88 121 136 148 176 187 242 272 296 374 407 484 592 629 748 814 968 1,258 1,496 1,628 1,936 2,057 2,516 2,992 3,256 4,114 4,477 5,032 6,512 6,919 8,228 8,954 10,064 13,838 16,456 17,908 27,676 32,912 35,816 55,352 71,632 76,109 110,704 152,218 304,436 608,872 1,217,744

Collatz Trajectory (204 steps to reach 1)

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

1,217,744 608,872 304,436 152,218 76,109 228,328 114,164 57,082 28,541 85,624 42,812 21,406 10,703 32,110 16,055 48,166 24,083 72,250 36,125 108,376 54,188 27,094 13,547 40,642 20,321 60,964 30,482 15,241 45,724 22,862 11,431 34,294 17,147 51,442 25,721 77,164 38,582 19,291 57,874 28,937 86,812 43,406 21,703 65,110 32,555 97,666 48,833 146,500 73,250 36,625 109,876 54,938 27,469 82,408 41,204 20,602 10,301 30,904 15,452 7,726

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