697,935

3 × 5 × 7 × 17² × 23

Starting at 697,935, the Collatz iteration reaches 1 after 136 steps. The first transition is 2093806; the starting value is odd with 48 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 7 × 17^2 × 23

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,414,656

Proper Divisor Sum 716,721

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #697913 ← → #697937

Radix Representation

Decimal	697935
Binary	10101010011001001111 (20 bits)
Octal	0o2523117
Hexadecimal	0xAA64F

Divisor Catalog (48)

1 3 5 7 15 17 21 23 35 51 69 85 105 115 119 161 255 289 345 357 391 483 595 805 867 1,173 1,445 1,785 1,955 2,023 2,415 2,737 4,335 5,865 6,069 6,647 8,211 10,115 13,685 19,941 30,345 33,235 41,055 46,529 99,705 139,587 232,645 697,935

Collatz Trajectory (136 steps to reach 1)

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

697,935 2,093,806 1,046,903 3,140,710 1,570,355 4,711,066 2,355,533 7,066,600 3,533,300 1,766,650 883,325 2,649,976 1,324,988 662,494 331,247 993,742 496,871 1,490,614 745,307 2,235,922 1,117,961 3,353,884 1,676,942 838,471 2,515,414 1,257,707 3,773,122 1,886,561 5,659,684 2,829,842 1,414,921 4,244,764 2,122,382 1,061,191 3,183,574 1,591,787 4,775,362 2,387,681 7,163,044 3,581,522 1,790,761 5,372,284 2,686,142 1,343,071 4,029,214 2,014,607 6,043,822 3,021,911 9,065,734 4,532,867 13,598,602 6,799,301 20,397,904 10,198,952 5,099,476 2,549,738 1,274,869 3,824,608 1,912,304 956,152

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