782,019

3² × 7 × 12413

782,019 factors as 3^2 × 7 × 12413. Its 12 positive divisors give a proper-divisor sum of 509,037, so this integer is deficient. The Collatz stopping time is 224 steps.

Prime Factor Structure

Factorization String 3^2 × 7 × 12413

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 1,291,056

Proper Divisor Sum 509,037

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #782011 ← → #782053

Radix Representation

Decimal	782019
Binary	10111110111011000011 (20 bits)
Octal	0o2767303
Hexadecimal	0xBEEC3

Divisor Catalog (12)

1 3 7 9 21 63 12,413 37,239 86,891 111,717 260,673 782,019

Collatz Trajectory (224 steps to reach 1)

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

782,019 2,346,058 1,173,029 3,519,088 1,759,544 879,772 439,886 219,943 659,830 329,915 989,746 494,873 1,484,620 742,310 371,155 1,113,466 556,733 1,670,200 835,100 417,550 208,775 626,326 313,163 939,490 469,745 1,409,236 704,618 352,309 1,056,928 528,464 264,232 132,116 66,058 33,029 99,088 49,544 24,772 12,386 6,193 18,580 9,290 4,645 13,936 6,968 3,484 1,742 871 2,614 1,307 3,922 1,961 5,884 2,942 1,471 4,414 2,207 6,622 3,311 9,934 4,967

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