408,591

3³ × 37 × 409

408,591 factors as 3^3 × 37 × 409. Its 16 positive divisors give a proper-divisor sum of 214,609, so this integer is deficient. The Collatz stopping time is 161 steps.

Prime Factor Structure

Factorization String 3^3 × 37 × 409

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 623,200

Proper Divisor Sum 214,609

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #408563 ← → #408607

Radix Representation

Decimal	408591
Binary	1100011110000001111 (19 bits)
Octal	0o1436017
Hexadecimal	0x63C0F

Divisor Catalog (16)

1 3 9 27 37 111 333 409 999 1,227 3,681 11,043 15,133 45,399 136,197 408,591

Collatz Trajectory (161 steps to reach 1)

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

408,591 1,225,774 612,887 1,838,662 919,331 2,757,994 1,378,997 4,136,992 2,068,496 1,034,248 517,124 258,562 129,281 387,844 193,922 96,961 290,884 145,442 72,721 218,164 109,082 54,541 163,624 81,812 40,906 20,453 61,360 30,680 15,340 7,670 3,835 11,506 5,753 17,260 8,630 4,315 12,946 6,473 19,420 9,710 4,855 14,566 7,283 21,850 10,925 32,776 16,388 8,194 4,097 12,292 6,146 3,073 9,220 4,610 2,305 6,916 3,458 1,729 5,188 2,594

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