406,175

5² × 7 × 11 × 211

Starting at 406,175, the Collatz iteration reaches 1 after 267 steps. The first transition is 1218526; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 5^2 × 7 × 11 × 211

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 630,912

Proper Divisor Sum 224,737

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #406171 ← → #406177

Radix Representation

Decimal	406175
Binary	1100011001010011111 (19 bits)
Octal	0o1431237
Hexadecimal	0x6329F

Divisor Catalog (24)

1 5 7 11 25 35 55 77 175 211 275 385 1,055 1,477 1,925 2,321 5,275 7,385 11,605 16,247 36,925 58,025 81,235 406,175

Collatz Trajectory (267 steps to reach 1)

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

406,175 1,218,526 609,263 1,827,790 913,895 2,741,686 1,370,843 4,112,530 2,056,265 6,168,796 3,084,398 1,542,199 4,626,598 2,313,299 6,939,898 3,469,949 10,409,848 5,204,924 2,602,462 1,301,231 3,903,694 1,951,847 5,855,542 2,927,771 8,783,314 4,391,657 13,174,972 6,587,486 3,293,743 9,881,230 4,940,615 14,821,846 7,410,923 22,232,770 11,116,385 33,349,156 16,674,578 8,337,289 25,011,868 12,505,934 6,252,967 18,758,902 9,379,451 28,138,354 14,069,177 42,207,532 21,103,766 10,551,883 31,655,650 15,827,825 47,483,476 23,741,738 11,870,869 35,612,608 17,806,304 8,903,152 4,451,576 2,225,788 1,112,894 556,447

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