2,771,769

3 × 7 × 11 × 13² × 71

Starting at 2,771,769, the Collatz iteration reaches 1 after 306 steps. The first transition is 8315308; the starting value is odd with 48 positive divisors.

Prime Factor Structure

Factorization String 3 × 7 × 11 × 13^2 × 71

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 5,059,584

Proper Divisor Sum 2,287,815

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #2771767 ← → #2771773

Radix Representation

Decimal	2771769
Binary	1010100100101100111001 (22 bits)
Octal	0o12445471
Hexadecimal	0x2A4B39

Divisor Catalog (48)

1 3 7 11 13 21 33 39 71 77 91 143 169 213 231 273 429 497 507 781 923 1,001 1,183 1,491 1,859 2,343 2,769 3,003 3,549 5,467 5,577 6,461 10,153 11,999 13,013 16,401 19,383 30,459 35,997 39,039 71,071 83,993 131,989 213,213 251,979 395,967 923,923 2,771,769

Collatz Trajectory (306 steps to reach 1)

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

2,771,769 8,315,308 4,157,654 2,078,827 6,236,482 3,118,241 9,354,724 4,677,362 2,338,681 7,016,044 3,508,022 1,754,011 5,262,034 2,631,017 7,893,052 3,946,526 1,973,263 5,919,790 2,959,895 8,879,686 4,439,843 13,319,530 6,659,765 19,979,296 9,989,648 4,994,824 2,497,412 1,248,706 624,353 1,873,060 936,530 468,265 1,404,796 702,398 351,199 1,053,598 526,799 1,580,398 790,199 2,370,598 1,185,299 3,555,898 1,777,949 5,333,848 2,666,924 1,333,462 666,731 2,000,194 1,000,097 3,000,292 1,500,146 750,073 2,250,220 1,125,110 562,555 1,687,666 843,833 2,531,500 1,265,750 632,875

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