λ
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Atlas › Integer Profiles › Node 33,221,825

33,221,825

52 × 7 × 13 × 17 × 859
Deficient Odd Composite

33,221,825 factors as 5^2 × 7 × 13 × 17 × 859. Its 48 positive divisors give a proper-divisor sum of 20,524,735, so this integer is deficient. The Collatz stopping time is 263 steps.

Prime Factor Structure

Factorization String 5^2 × 7 × 13 × 17 × 859
Distinct Prime Factors 5
Square Status No
Abundance Measure Deficient

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 53,746,560
Proper Divisor Sum 20,524,735
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #33221813 ← → #33221833

Radix Representation

Decimal 33221825
Binary 1111110101110110011000001 (25 bits)
Octal 0o176566301
Hexadecimal 0x1FAECC1

Divisor Catalog (48)

1 5 7 13 17 25 35 65 85 91 119 175 221 325 425 455 595 859 1,105 1,547 2,275 2,975 4,295 5,525 6,013 7,735 11,167 14,603 21,475 30,065 38,675 55,835 73,015 78,169 102,221 150,325 189,839 279,175 365,075 390,845 511,105 949,195 1,328,873 1,954,225 2,555,525 4,745,975 6,644,365 33,221,825

Collatz Trajectory (263 steps to reach 1)

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

33,221,825 99,665,476 49,832,738 24,916,369 74,749,108 37,374,554 18,687,277 56,061,832 28,030,916 14,015,458 7,007,729 21,023,188 10,511,594 5,255,797 15,767,392 7,883,696 3,941,848 1,970,924 985,462 492,731 1,478,194 739,097 2,217,292 1,108,646 554,323 1,662,970 831,485 2,494,456 1,247,228 623,614 311,807 935,422 467,711 1,403,134 701,567 2,104,702 1,052,351 3,157,054 1,578,527 4,735,582 2,367,791 7,103,374 3,551,687 10,655,062 5,327,531 15,982,594 7,991,297 23,973,892 11,986,946 5,993,473 17,980,420 8,990,210 4,495,105 13,485,316 6,742,658 3,371,329 10,113,988 5,056,994 2,528,497 7,585,492

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